FOR THE
IB DIPLOMA
PROGRAMME
THIRD EDITION
Physics
John Allum and Paul Morris
Practice
Exam-style
Questions
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Contents
A
Space, time and motion
A.1
Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A.2
Forces and momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
A.3
Work, energy and power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
A.4
Rigid body mechanics (HL only) . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
A.5
Relativity (HL only) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
B
The particulate nature of matter
B.1
Thermal energy transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
B.2
Greenhouse effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
B.3
Gas laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
B.4
Thermodynamics (HL only) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
B.5
Current and circuits (includes HL section). . . . . . . . . . . . . . . . . . . . 16
C
Wave behaviour
C.1
Simple harmonic motion (includes HL section) . . . . . . . . . . . . . . . . 19
C.2
Wave model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
C.3
Wave phenomena (includes HL section) . . . . . . . . . . . . . . . . . . . . . 23
C.4
Standing waves and resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
C.5
Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
D
Fields
D.1
Gravitational fields (includes HL section) . . . . . . . . . . . . . . . . . . . . 29
D.2
Electric and magnetic fields (includes HL section) . . . . . . . . . . . . . . 31
D.3
Motion in electromagnetic fields. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
D.4
Induction (includes HL section). . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
E
Nuclear and quantum physics
E.1
Structure of the atom (includes HL section) . . . . . . . . . . . . . . . . . . . 37
E.2
Quantum physics (HL only) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
E.3
Radioactive decay (includes HL section) . . . . . . . . . . . . . . . . . . . . . 40
E.4
Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
E.5
Fusion and stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
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A.1 Kinematics
■ Paper 1
1 An object is thrown from a cliff at an angle to the
horizontal. The ground below the cliff is horizontal.
Three quantities are known about the motion.
I
The horizontal component of the initial velocity of
the object
II The initial angle between the velocity of the object
and the horizontal
III The height of the cliff
What are the quantities that must be known in order
to determine the horizontal distance from the point of
projection to the point where the object hits the ground?
A I and II only
B I and III only
C II and III only
D I, II and III
4 A girl throws an object horizontally at time t = 0.
Air resistance can be ignored. At t = 0.50 s the object
travels horizontally a distance x in metres while it falls
vertically through a distance y in metres.
What is the initial velocity of the object and the vertical
distance fallen at t = 1.0 s?
Initial velocity / m s−1
Vertical distance fallen / m
A
x
2y
B
x
4y
C
2x
2y
D
2x
4y
Paper 1, TZ1, May 2019, Q5
5 The variation with time t of the acceleration a of an
object is shown.
Paper 1, May 2019, Q4
2 A sports car is accelerated from 0 to 100 km per hour in
3 s. What is the acceleration of the car?
A 0.1g
B 0.3g
C 0.9g
D 3g
Paper 1, TZ1, May 2019, Q4
3 A truck has an initial speed of 20 m s−1. It decelerates at
4.0 m s−2.
What is the distance taken by the truck to stop?
A 2.5 m
B 5.0 m
C 50 m
D 100 m
Paper 1, TZ1, November 2018, Q3
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What is the change of velocity of the object from t = 0 to
t = 6s?
A 6 m s−1
B 8 m s−1
C 10 m s−1
D 14 m s−1
Paper 1, November 2019, Q4
A.1 Kinematics
1
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■ Paper 2
1 Two players are playing table tennis. Player A hits the ball at a height of 0.24 m above the
edge of the table, measured from the top of the table to the bottom of the ball. The initial
speed of the ball is 12.0 m s−1 horizontally. Assume that air resistance is negligible.
12.0 m s–1
diagram not to scale
0.24 m
table
net
a Show that the time taken for the ball to reach the
surface of the table is about 0.2 s.
[1]
b Make a sketch of the axes shown below and add a
line to show the variation with time of the vertical
component of velocity vv of the ball until it reaches
the table surface. [2]
vV /m s−1
3
2
1
0
0
0.1
Paper 2, TZ1, May 2021, Q1 (part)
2 A truck is travelling along a horizontal straight road
with a constant speed of 15.0 m s−1. As it passes a
stationary car, the car begins to accelerate at a constant
2.4 m s−2.
a After 10 s, the truck has travelled 150 m.
i What is the speed of the car at this time?
[2]
ii How far has the car travelled in this time?
[2]
b After 10 s, the car continues travelling at a constant
speed. Sketch speed–time graphs (on the same
axes) for the two vehicles for the 15 s after the car
started moving.
[3]
c At what time were the two vehicles moving with
the same speed?
[1]
d After how many seconds will the car overtake
the truck?
[3]
0.2
Time/s
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c The net is stretched across the middle of the table.
The table has a length of 2.74 m and the net has a
height of 15.0 cm.
Show that the ball will go over the net.
[3]
A.1 Kinematics
2
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A.2 Forces and momentum
■ Paper 1
1 A waiter carrying a tray is accelerating to the right as
shown in the image. What is the free-body diagram of
the forces acting on the tray?
velocity
Force for first 2.0 s / N
Force for second 2.0 s / N
A
10
0
B
20
40
C
10
40
D
20
0
Paper 1, TZ2, May 2019, Q6
4 Three forces act a point. In which diagram is the point
in equilibrium?
F2
A
F2
B
F3
F3
F1
A
B
C
D
F1
Paper 1, TZ1, May 2019, Q7
2 An object of mass 8.0 kg is falling vertically through the
air. The drag force acting on the object is 60 N. What is
the best estimate of the acceleration of the object?
A zero
B 2.5 m s−2
C 7.5 m s−2
D 10 m s−2
Paper 1, November 2020, Q5
3 The graph shows the variation of momentum with time
of an object.
C
D
F2
F2
F3
F3
F1
F1
Paper 1, November 2018, Q7
5 A ball rolls on the floor towards a wall and rebounds
with the same speed and at the same angle to the wall.
Momentum/kg m s–1
What net force acts on the object for the first 2.0 s and
second 2.0 s of the motion?
20
What is the direction of the impulse applied to the ball
by the wall?
A
0
0
2.0
4.0
Time/s
D
B
C
Paper 1, November 2021, Q7
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A.2 Forces and momentum
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■ Paper 2
1 A company delivers packages to customers using a
small pilotless aircraft. Rotating horizontal blades exert
a force on the surrounding air. The air above the aircraft
is initially stationary.
aircraft
2 The Rotor is an amusement park ride that can be
modelled as a vertical cylinder of inner radius R rotating
about its axis. When the cylinder rotates sufficiently
fast, the floor drops out and the passengers stay
motionless against the inner surface of the cylinder. The
diagram shows a person taking the Rotor ride. The floor
has been lowered away from the person.
axis of rotation
R
package
ground
The air is propelled vertically downwards with speed v.
The aircraft hovers motionless above the ground. A
package is suspended from the aircraft on a string. The
mass of the aircraft is 0.95 kg and the combined mass of
the package and the string is 0.45 kg. The mass of the air
pushed downwards by the blades in one second is 1.7 kg.
a State the value of the resultant force on the aircraft
when hovering.
[1]
b Outline, by reference to Newton’s third law, how the
upward lift force on the aircraft is achieved.
[2]
c Determine v. State your answer to an appropriate
number of significant figures.
[3]
d The package and string are now released and fall
to the ground. The lift force on the aircraft remains
unchanged. Calculate the initial acceleration of
the aircraft.
[2]
Paper 2, November 2020, Q1 (part)
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a Draw and label a free-body diagram for the person.
[2]
b The person must not slide down the wall. Show that
the minimum angular velocity ω of the cylinder for
this situation is:
g
ω=
μR
where μ is the coefficient of static friction between
the person and the cylinder.
[2]
c The coefficient of static friction between the person
and the cylinder is 0.40. The radius of the cylinder is
3.5 m. The cylinder makes 28 revolutions per minute.
Deduce whether the person will slide down the inner
surface of the cylinder.
[3]
Paper 2, November 2020, Q2
A.2 Forces and momentum
4
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A.3 Work, energy and power
■ Paper 1
1 An object has a weight of 6.10 × 102 N. What is the
change in gravitational potential energy when it moves
through 8.0 m vertically?
A 5 kJ
B 4.9 kJ
C 4.88 kJ
D 4.880 kJ
Paper 1, TZ2, May 2019, Q5
4 A car is driven from rest along a straight horizontal
road. The car engine exerts a constant driving force.
Friction and air resistance are negligible. How does the
power developed by engine change with the distance
travelled?
A Power does not change.
B Power decreases linearly.
C Power increases linearly.
D Power increases non-linearly.
Paper 1, November 2020, Q5
a/m s–2
2 A force acts on an object of mass 40 kg. The graph
shows how the acceleration a of the object varies with
its displacement, d.
20
5 What is the unit of power expressed in fundamental
SI units?
A kg m s
B kg m2 s−2
C kg m s−3
D kg m2 s−3
Paper 1, November 2018, Q1
10
■ Paper 2
0
0
2
4
d/m
What is the work done by the force on the object?
A 50 J
B 2000 J
C 2400 J
D 3200 J
Paper 1, TZ1, May 2021, Q7
3 A compressed spring is used to launch an object along
a horizontal frictionless surface. When the spring is
compressed through a distance x and released, the
object leaves the spring at speed v. What is the distance
through which the spring must be compressed for the
v
object to leave the spring at ?
2
A
x
4
B
x
2
C
x
2
1 A car of mass 1200 kg is travelling up a uniform slope
with a constant speed of 15 m s−1. The car takes 30 s to
increase its vertical height by 20 m.
a If the resistive forces opposing the motion of the car
have a total of 2200 N, what output power from the
car is needed to overcome these forces?
[1]
b Calculate the gravitational potential energy gained
by the car in 30 s.
[1]
c Calculate the total output power needed by the car
to overcome the resistive forces and to rise a vertical
height of 20 m.
[2]
d If the input power to the car is 120 kW, draw a
Sankey diagram to represent the principal energy
transfers.[4]
2 a What do you understand by the mechanical energy
of a system?
[2]
b Under what circumstances will the mechanical
energy of a system be conserved?
[1]
c A steel spring which has a spring constant of
74 N m−1 was stretched by 8.0 cm.
i How much energy was stored in the spring? [2]
ii What assumption did you make in answering
part i?[1]
D x 2
Paper 1, November 2018, Q6
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A.3 Work, energy and power
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■ Data-based question
1 In an experiment to measure the acceleration of free fall
a student ties two different blocks of masses m1 and m2 to
the ends of a string that passes over a frictionless pulley.
a In a particular experiment the student calculates
that a = (0.204 ± 0.002) ms–2 using
m1 = (0.125 ± 0.001) kg and m2 = (0.120 ± 0.001) kg.
i
Calculate the percentage uncertainty in the
measured value of g.[3]
ii Deduce the value of g and its absolute
uncertainty for this experiment.
[2]
b There is an advantage and a disadvantage in using
two masses that are almost equal.
State and explain,
i
The student calculates the acceleration a of the blocks
by measuring the time taken by the heavier mass to
fall through a given distance. Their theory predicts that
m – m2
a=g 1
and this can be rearranged to give
m1 + m2
m + m2
g=a 1
.
m1 – m2
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the advantage with reference to the magnitude of
the acceleration that is obtained.
[2]
ii the disadvantage with reference to your answer
to aii.[2]
Paper 3, TZ1, May 2019, Q3
A.3 Work, energy and power
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A.4 Rigid body mechanics (HL only)
■ Paper 1
■ Paper 2
1 Torque is the rotational analogue of the linear
motion quantity:
A momentum
B acceleration
C force
D impulse
1 A solid cylinder of mass M and radius R rolls without
slipping down a uniform slope. The slope makes an
angle θ to the horizontal.
N
2 A wheel of mass m and radius r was rolling on
a flat horizontal surface without slipping. If the
angular velocity of the wheel was ω, what was its
linear momentum?
A mωr
mω
B
r
C mω2r
mω2
D
r
3 A solid sphere of mass m, constant density and radius
2
r has a moment of inertia of I = mr2 about an axis
5
through its centre. What would be the moment of
inertia of a sphere of the same material, but with double
the radius?
A 2I
B 4I
C 8I
D 32I
4 An object was rotating at 20 rad s−1. A constant torque of
10 Nm then accelerated it to 60 rad s−1 in 2.0 s. What was
the moment of inertia of the object?
A 0.5 kg m2
B 1.0 kg m2
C 2.0 kg m2
D 3.0 kg m2
5 This system is in equilibrium.
R2
Which of the following must be true
if 2R1 = R2?
A m1= m2
B R1m1 = R2m2
C 2R1m1 = R2m2
D 2R1m1 = 2R2m2
R1
F
θ
Mg
The diagram shows the three forces acting on the
cylinder. N is the normal reaction force and F is the
frictional force between the cylinder and the slope.
a State why F is the only force providing a torque
about the axis of the cylinder.
b i
[1]
The moment of inertia of a cylinder about its axis
1
is I = MR2. Show that, by applying Newton’s
2
laws of motion, the linear acceleration of the
2
cylinder is a = g sin θ.[4]
3
ii Calculate, for θ = 30°, the time it takes for the
solid cylinder to travel 1.5 m along the slope.
The cylinder starts from rest.
[2]
c A block of ice is placed on the slope beside the solid
cylinder and both are released at the same time. The
block of ice is the same mass as the solid cylinder
and slides without friction.
At any given point on the slope, the speed of the
block of ice is greater than the speed of the solid
cylinder. Outline why, using the answer to bi.[1]
d The solid cylinder is replaced by a hollow cylinder of
the same mass and radius. Suggest how this change
will affect, if at all, the acceleration in bi.[2]
Paper 3, May 2016, Q8 (part)
m1
m2
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A.4 Rigid body mechanics (HL only)
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2 A uniform rod of weight 36.0 N and length 5.00 m
rests horizontally. The rod is pivoted at its left-hand
end and is supported at a distance of 4.00 m from the
frictionless pivot.
5.00 m
4.00 m
pivot
support
a Calculate the force the support exerts on the rod. [2]
b The support is suddenly removed and the rod begins
to rotate clockwise about the pivot point. The moment
of inertia of the rod about the pivot point is 30.6 kg m2.
i Calculate, in rad s–2, the initial angular
acceleration α of the rod.
[2]
ii After time t the rod makes an angle θ with the
1
horizontal. Outline why the equation θ = αt2
2
cannot be used to find the time it takes θ to
π
become (that is for the rod to become vertical
2
for the first time).
[2]
c At the instant the rod becomes vertical:
i show that the angular speed is ω = 2.43 rad s–1.[3]
ii calculate the angular momentum of the rod. [1]
Paper 3, November 2018, Q8
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A.4 Rigid body mechanics (HL only)
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A.5 Relativity (HL only)
1 The special theory of relativity:
A only applies for objects moving at very high speeds.
B has not been experimentally verified.
C can be applied to all moving objects.
D only applies to subatomic particles.
2 A spaceship is 120 m long when measured at rest.
What is its length as measured by observers who see
the spaceship moving past them at 99% of the speed
of light?
A 170 m
B 17 m
C 1700 m
D 1.7 m
3 If a spacecraft approaches a light beacon at a speed of
0.4c, observers on the spacecraft will measure the speed
of light arriving at them to be:
A c
B 0.4c
C 0.6c
D 1.4c
4 An inertial reference frame:
A is always on the Earth’s surface.
B is not accelerating.
C is at infinity.
D is not moving with respect to the observer.
5 A star in a distant galaxy is estimated to have a lifetime
of 20 billion years. The star is moving away from Earth
at a speed of 0.75c. Determine an estimated lifetime for
the star according to an astronomer on Earth.
A 14 billion years
B 17 billion years
C 24 billion years
D 30 billion years
■ Paper 2
1 Muons are created at a height of 3230 m above the
Earth’s surface. The muons move vertically downward
at a speed of 0.980c relative to the Earth’s surface. The
gamma factor for this speed is 5.00. The half-life of a
muon in its rest frame is 2.20 μs.
a Estimate in the Earth frame the fraction of the
original muons that will reach the Earth’s surface
before decaying according to:
i Newtonian mechanics
[2]
ii special relativity.
[2]
b Demonstrate how an observer moving with the same
velocity as the muons accounts for the answer to
part a ii.[2]
Paper 3, TZ1, May 2019, Q4
2 The spacetime diagram is in the reference frame of
an observer O on Earth. Observer O and spaceship A
are at the origin of the space–time diagram when time
t = t′ = 0. The worldline for spaceship A is shown.
ct/ly
■ Paper 1
ct’
10
8
6
4
2
0
0
2
4
6
8
10
x/ly
Calculate in terms of c the velocity of spaceship
A relative to observer O.
[1]
ii Copy the diagram and draw the x′-axis for the
reference frame of spaceship A.
[1]
b Event E is the emission of a flash of light. Observer
O sees light from the flash when t = 9 years and
calculates that event E is 4 ly away, in the positive
x-direction.
i Plot Event E on the spacetime diagram and
label it E.
[2]
ii Determine the time, according to spaceship A,
when light from Event E was observed on
spaceship A.
[3]
a i
Paper 2, November 2020, Q5
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A.5 Relativity (HL only)
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B.1 Thermal energy transfers
1 Energy is transferred to water in a flask at a rate P. The
water reaches boiling point and then P is increased.
What are the changes to the temperature of the water
and to the rate of vaporization of the water after the
change?
Temperature
Rate of vaporization
A
increases
unchanged
B
increases
increases
C
unchanged
unchanged
D
unchanged
increases
Paper 1, TZ1, May 2019, Q10
2 When 40 kJ of energy is transferred to a quantity of a
liquid substance, its temperature increases by 20 K. When 600 kJ of energy is transferred to the same
quantity of the liquid at its boiling temperature, it
vaporizes completely at constant temperature.
What is the specific latent heat of vaporization / specific
heat capacity of the liquid for this substance?
A 15 K−1
B 15 K
C 300 K−1
D 300 K
Paper 1, TZ1, May 2021, Q9
3 A piece of metal at a temperature of 100 °C is dropped
into an equal mass of water at a temperature of 15 °C
in a container of negligible mass. The specific heat
capacity of water is four times that of the metal. What is
the final temperature of the mixture?
A 83 °C
B 57 °C
C 45 °C
D 32 °C
Paper 1, TZ2, May 2021, Q12
4 Thermal energy flowed at a rate of 100 W through a
wall when its outside surface temperature was −10 °C
and the inside surface temperature was 20 °C.
At what inside surface temperature would the flow of
thermal energy be reduced to 50 W?
A 0 °C
B 5 °C
C 10 °C
D 15 °C
5 A surface has a temperature of 20 °C. It emits thermal
radiation at a rate of 50 W.
At what temperature would the same surface emit
thermal energy at a rate of 100 W?
A 24 °C
B 40 °C
C 75 °C
D 320 °C
Paper 1, November 2019, Q16
■ Paper 2
1 The luminosity of a particular star is 5.5 × 1027 W.
a Explain what is meant by luminosity.
[2]
b The spectrum of radiation received from the same
star has its maximum intensity at a wavelength of
4.9 × 10−7 m. Determine the surface temperature
of the star.
[1]
−7
c The apparent brightness of the star is 1.5 × 10 in
SI units. What are the SI units for apparent
brightness?
[1]
d Determine the distance from Earth to the star in
light-years.
[3]
2 A sample of vegetable oil, initially in the liquid state, is
placed in a freezer that transfers thermal energy from
the sample at a constant rate. The graph shows how
temperature T of the sample varies with time t.
T/K
■ Paper 1
290
270
250
230
0
10
20
30
40
50 60
t/minutes
The following data is available.
Mass of the sample = 0.32 kg
Specific latent heat of fusion of the oil = 130 kJ kg–1
Rate of thermal energy transfer = 15 W
a i Calculate the thermal energy transferred from
the sample during the first 30 minutes.
[1]
ii Estimate the specific heat capacity of the oil in
its liquid phase. State an appropriate unit for
your answer.
[2]
b The sample begins to freeze during the thermal
energy transfer. Explain, in terms of the molecular
model of matter, why the temperature of the sample
remains constant during freezing.
[3]
c Calculate the mass of the oil that remains unfrozen
after 60 minutes.
[2]
Paper 2, November 2020, Q3
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B.1 Thermal energy transfers
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B.2 Greenhouse effect
■ Paper 1
1 What is the main role of carbon dioxide in the
greenhouse effect?
A It absorbs incoming radiation from the Sun.
B It absorbs outgoing radiation from the Earth.
C It reflects incoming radiation from the Sun.
D It reflects outgoing radiation from the Earth.
Paper 1, TZ2, May 2021, Q24
2 Light of intensity I 0 is incident on a snow-covered area
of Earth. In a model of this situation, the albedo of the
cloud is 0.30 and the albedo for the snow surface is 0.80.
What is the intensity of the light at P due to the incident
ray I 0?
C 10% of the radiation incident on the Moon is
reflected by its surface.
D 10% of the radiation emitted by the Moon is at
infrared wavelengths.
Paper 1, November 2019, Q30
4 The diagram shows a simple model of the energy
balance in the Earth surface–atmosphere system. The
intensities of the radiations are given.
What is the average intensity radiated by the atmosphere
towards the surface?
A 100 W m–2
B 150 W m–2
C 240 W m–2
D 390 W m–2
reflected
100 W m–2
outgoing
240 W m–2
incoming
340 W m–2
atmosphere
surface
absorption
240 W m–2
surface
reflection
390 W m–2
radiated
by
atmosphere
surface
A 0.14 I 0
B 0.24 I 0
C 0.50 I 0
D 0.55 I 0
Paper 1, November 2021 Q25
Paper 1, November 2018, Q25
3 What is meant by the statement that the average albedo
of the Moon is 0.1?
A 10% of the radiation incident on the Moon is
absorbed by its surface.
B 10% of the radiation emitted by the Moon is
absorbed by its atmosphere.
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5 Most power stations rely on a turbine and generator to
produce electrical energy. Which power station works
on a different principle?
A Nuclear
B Solar
C Fossil fuel
D Wind
Paper 1, TZ1, May 2019, Q25
B.2 Greenhouse effect
11
16/02/2023 20:33
■ Paper 2
1 The average temperature of ocean surface water is
289 K. Oceans behave as black bodies.
a Show that the intensity radiated by the oceans is
about 400 W m−2.
[1]
b Explain why some of this radiation is returned to the
oceans from the atmosphere.
[3]
c The intensity in part b returned to the oceans is
330 W m−2. The intensity of the solar radiation
incident on the oceans is 170 W m−2.
i Calculate the additional intensity that must be
lost by the oceans so that the water temperature
remains constant.
[2]
ii Suggest a mechanism by which the additional
intensity can be lost. [1]
Paper 2, TZ2, May 2019, Q7
2 The Moon has no atmosphere and orbits the Earth. The
diagram shows the Moon with rays of light from the
Sun that are incident at 90° to the axis of rotation of
the Moon.
axis of rotation
B
to Sun
A
Moon
A black body is on the Moon’s surface at point
A. Show that the maximum temperature that
this body can reach is 400 K. Assume that the
Earth and the Moon are the same distance from
the Sun.
[2]
ii Another black body is on the Moon’s surface at
point B. Outline, without calculation, why the
maximum temperature of the black body at point
B is less than at point A.
[2]
b The albedo of the Earth’s atmosphere is 0.28.
Outline why the maximum temperature of a black
body on the Earth when the Sun is overhead is less
than that at point A on the Moon.
[1]
a i
Paper 2, TZ1, May 2019, Q7
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B.2 Greenhouse effect
12
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B.3 Gas laws
■ Paper 1
1 A gas storage tank of fixed volume V contains N
molecules of an ideal gas at temperature T. The pressure
at kelvin temperature T is 20 MPa.
N
molecules are removed and the temperature changed
4
to 2T. What is the new pressure of the gas?
A 10 Mpa
B 15 Mpa
C 30 Mpa
D 40 Mpa
Paper 1, TZ1, May 2019, Q12
2 Two ideal gases X and Y are at the same temperature.
The mass of a particle of gas X is larger than the mass
of a particle of gas Y. Which is correct about the average
kinetic energy and the average speed of the particles in
gases X and Y?
Average kinetic energy
Average speed
A
Larger for Y
Larger for Y
B
Same
Larger for Y
C
Same
Same
D
Larger for Y
same
Paper 1, TZ1, May 2021, Q10
3 Container X contains 1.0 mol of an ideal gas. Container
Y contains 2.0 mol of the ideal gas. Y has four times the
volume of X. The pressure in X is twice that in Y.
temperature of gas in X
What is =
?
temperature of gas in Y
1
A
4
1
B
2
C 1
D 2
4 The molar mass of an ideal gas is M. A fixed mass m
of the gas expands at a constant pressure P. The graph
shows the variation with temperature T of the gas
volume V.
V
0
0
T
What is the gradient of the graph?
MP
A
mR
B
C
D
MR
mP
mP
MR
mR
MP
Paper 1, November 2021, Q10
5 The average translational speed of molecules in an ideal
gas is 500 m s−1. Which of the following is correct?
A The pressure of the gas will be 8.3 × 104 Pa when the
density of the gas is 0.5 kg m−3.
B The pressure of the gas will be 8.3 × 104 Pa when the
density of the gas is 1.0 kg m−3.
C The pressure of the gas will be 4.2 × 104 Pa when the
density of the gas is 2.0 kg m−3.
D The pressure of the gas will be 1.0 × 106 Pa when the
density of the gas is 4.0 kg m−3.
Paper 1, November 2018, Q12
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B.3 Gas laws
13
16/02/2023 20:33
■ Data-based question
1 A container of volume 3.2 × 10 m is filled with helium
gas at a pressure of 5.1 × 105 Pa and temperature 320 K.
Assume that this sample of helium gas behaves as an
ideal gas.
a The mass of a helium atom is 6.6 × 10−27 kg.
Estimate the average speed of the helium atoms in
the container.
[2]
b Show that the number of helium atoms in the
container is 4 × 1020.
[2]
−31
3
c A helium atom has a volume of 4.9 × 10 m .
i Calculate the ratio of volume of helium atoms
to volume of helium gas.
[1]
ii Discuss, by reference to the kinetic model of an
ideal gas and the answer to part c i, whether the
assumption that helium behaves as an ideal gas
is justified.
[2]
−6
3
1 A spherical soap bubble is made of a thin film of soapy
water. The bubble has an internal air pressure Pi and is
formed in air of constant pressure Po. The theoretical
prediction for the variation of (Pi – Po) is given by
the equation
4γ
(Pi – Po) =
R
where γ is a constant for the thin film and R is the radius
of the bubble.
Data for (Pi – Po) and R were collected under controlled
conditions and plotted as a graph showing the variation
1
of (Pi – Po) with .
R
(Pi – Po)/Pa
■ Paper 2
3.00
2.50
Paper 2, TZ2, May 2019, Q2
2 The air in a kitchen has pressure 1.0 × 105 Pa and
temperature 22 °C. A refrigerator of internal volume
0.36 m3 is installed in the kitchen.
a With the door open the air in the refrigerator is
initially at the same temperature and pressure as the
air in the kitchen. Calculate the number of molecules
of air in the refrigerator.
[2]
b The refrigerator door is closed. The air in the
refrigerator is cooled to 5.0 °C and the number of air
molecules in the refrigerator stays the same.
i Determine the pressure of the air inside the
refrigerator.
[2]
ii The door of the refrigerator has an area of
0.72 m2. Show that the minimum force needed to
open the refrigerator door is about 4 kN.
[2]
iii Comment on the magnitude of the force in
part b ii.
[2]
Paper 2, November 2019, Q2
2.00
1.50
1.00
0.50
0.00
10.00
12.50
15.00
17.50
20.00
22.50
25.00
R–1/m–1
a Suggest whether the data are consistent with the
theoretical prediction.
[2]
b i
Show that the value of γ is about 0.03.
ii Identify the fundamental units of γ.
[2]
[1]
iii In order to find the uncertainty for γ, a maximum
gradient line would be drawn.
On the graph, sketch the maximum gradient line
for the data.
[1]
iv The percentage uncertainty for γ is 15%. State γ,
with its absolute uncertainty.
[2]
v The expected value of γ is 0.027. Comment on
your result.
[1]
Paper 3, November 2020, Q1
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B.3 Gas laws
14
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B.4 Thermodynamics (HL only)
■ Paper 1
1 The entropy of a non-isolated system can decrease if:
A a process is done very quickly.
B energy is conserved.
C the entropy of the surroundings decreases by a
greater amount.
D the entropy of the surroundings increases by at least
the same amount.
2 12 J of work were done by an ideal gas as its internal
energy decreased by 4 J.
The thermal energy transferred into the gas was:
A +8 J
B −8 J
C +16 J
D −16 J
3 The temperature of 2.0 mol of an ideal gas was increased
from 280 K to 290 K. What is the best estimate for the
increase in internal energy of the gas?
A 20 J
B 250 J
C 23 000 J
D 24 000 J
4 The first law of thermodynamics is an application of:
A the principle of conservation of energy.
B the Carnot cycle.
C the principle that entropy always increases.
D the fact that thermal energy always spontaneously
moves from hotter places to cooler places.
5 The pressure of a gas is a constant 1.0 × 105 Pa. Its
volume decreases by 2.0 cm3. In this process:
A 2.0 × 10−1 J of work is done by the gas.
B 2.0 × 10−1 J of work is done on the gas.
C 2.0 × 105 J of work is done by the gas.
D 2.0 × 105 J of work is done on the gas.
■ Paper 2
Pressure/105 Pa
1 The diagram represents an ideal, monatomic gas that first
undergoes a compression, then an increase in pressure.
5
4
a Calculate the work done during the:
i compression
[1]
ii increase in pressure. [1]
b An adiabatic process then increases the volume of
the gas to 5.0 × 10 –2 m3.
i Calculate the pressure following this process. [2]
ii Outline how an approximate adiabatic change
can be achieved.
[2]
Paper 1, November 2020, Q11
2 a Show that during an adiabatic expansion of an ideal
monatomic gas the temperature T and volume V are
given by
2
TV 3 = constant
b The diagram shows a Carnot cycle for an ideal
monatomic gas.
P
[2]
A
B
D
C
V
The highest temperature in the cycle is 620 K and the
lowest is 340 K.
i Calculate the efficiency of the cycle.
[1]
ii The work done during the isothermal expansion
A → B is 540 J. Calculate the thermal energy that
leaves the gas during one cycle.
[2]
iii Calculate the ratio VC / VB where VC is the volume
of the gas at C and VB is the volume
at B.
[2]
c i Calculate the change in the entropy of the gas
during the change A to B.
[1]
ii Explain, by reference to the second law of
thermodynamics, why a real engine operating
between the temperatures of 620 K and 340 K
cannot have an efficiency greater than the
answer to part b i.
[2]
Paper 3, TZ1, May 2019, Q9
3
2
1
0
0
1
2
3
4
5
6
Volume/10–2m3
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B.4 Thermodynamics (HL only)
15
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B.5 Current and circuits
■ Paper 1
1 Two wires, X and Y, are made of the same material and
have equal length. The diameter of X is twice that of Y.
resistance of X
What is
?
resistance of Y
1
1
A
B
C 2
D 4
4
2
A
X
V
Paper 1, November 2021, Q19
2 A combination of four identical resistors each of
resistance R are connected to a source of emf ε of
negligible internal resistance. What is the current in the
resistor X?
e
What is the change in the reading on the ammeter and
the change in the reading on the voltmeter when the
light incident on X is increased?
Ammeter reading
Voltmeter reading
A
increases
decreases
B
increases
increases
C
decreases
decreases
D
decreases
increases
Paper 1, TZ2, May 2019, Q19
5 Two conductors S and T have the I–V characteristic
graphs shown below.
A
ε
5R
B
3ε
C
10R
2ε
D
5R
3ε
5R
Paper 1, November 2018, Q20
3 Two power supplies, one of constant emf 24 V and the
other of variable emf P, are connected to two resistors
as shown. Both power supplies have negligible internal
resistances.
I/A
X
8
7
6
S
T
5
4
3
2
1
9Ω
0
0
24 V
1
2
3
4
5
6
7
A
3Ω
P
What is the magnitude of P for the reading on the
ammeter to be zero?
A zero
B 6V
C 8V
D 18 V
Paper 1, November 2019, Q16
4 The resistance of component X decreases when the
intensity of light incident on it increases. X is connected
in series with a cell of negligible internal resistance and
a resistor of fixed resistance. The ammeter and voltmeter
are ideal.
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8
V /V
When the conductors are placed in the circuit below, the
reading of the ammeter is 6.0 A.
A
S
T
What is the emf of the cell?
A 4.0 V
B 5.0 V
C 8.0 V
D 13 V
Paper 1, TZ1, May 2021, Q16
B.5 Current and circuits
16
16/02/2023 20:33
■ Paper 2
1 A lighting system consists of two long metal rods with a
potential difference maintained between them. Identical
lamps can be connected between the rods as required.
power supply
c Cell X is replaced by a second cell of identical emf E
but with internal resistance 2.0 Ω.
Comment on the length of AC for which the current
in the second cell is zero.
[2]
Paper 2, TZ2, May 2018, Q4
rod
24 V, 5.0 W
rod
The following data is available for the lamps when at
their working temperature.
Lamp specifications 24 V, 5.0 W
Power supply emf 24 V
Power supply maximum current 8.0 A
Length of each rod 12.5 m
Resistivity of rod metal 7.2 × 10 –7 Ω m
a Each rod is to have a resistance no greater than
0.10 Ω. Calculate, in m, the minimum radius of each
rod. Give your answer to an appropriate number of
significant figures.
[3]
b Calculate the maximum number of lamps that can be
connected between the rods. Neglect the resistance
of the rods.
[2]
c One advantage of this system is that if one lamp
fails then the other lamps in the circuit remain lit.
Outline one other electrical advantage of this system
compared to one in which the lamps are connected
in series.
[1]
3 (This question requires knowledge from Theme A.)
A girl rides a bicycle that is powered by an electric
motor. A battery transfers energy to the electric motor.
The emf of the battery is 16 V and it can deliver a charge
of 43 kC when discharging completely from a full charge.
a The maximum speed of the girl on a horizontal road
is 7.0 m s–1 with energy from the battery alone. The
maximum distance that the girl can travel under
these conditions is 20 km.
i Show that the time taken for the battery to
discharge is about 3 × 103 s.
[1]
ii Deduce that the average power output of the
battery is about 240 W.
[2]
iii Friction and air resistance act on the bicycle
and the girl when they move. Assume that all
the energy is transferred from the battery to
the electric motor. Determine the total average
resistive force that acts on the bicycle and
the girl.
[2]
b The bicycle and the girl have a total mass of 66 kg.
The girl rides up a slope that is at an angle of 3.0° to
the horizontal.
Paper 2, November 2018, Q2 (part)
2 The diagram shows a potential divider circuit used to
measure the emf E of a cell X. Both cells have negligible
internal resistance.
C
cell X
A
Calculate the component of weight for the bicycle
and girl acting down the slope.
[1]
ii The battery continues to give an output power of
240 W. Assume that the resistive forces are the
same as in part a.
Calculate the maximum speed of the bicycle and
the girl up the slope.
[2]
i
B
12 V
3.0°
E
a State what is meant by the emf of a cell.
[2]
b AB is a wire of uniform cross-section and length
1.0 m. The resistance of wire AB is 80 Ω. When the
length of AC is 0.35 m the current in cell X is zero.
i
Show that the resistance of the wire AC
is 28 Ω.
ii Determine E.
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[2]
[2]
B.5 Current and circuits
17
16/02/2023 20:33
c On another journey up the slope, the girl carries an
additional mass. Explain whether carrying this mass
will change the maximum distance that the bicycle
can travel along the slope.
[2]
d The bicycle has a meter that displays the current and
the terminal potential difference (p.d.) for the battery
when the motor is running. The diagram shows the
meter readings at one instant. The emf of the cell
is 16 V.
pd
current
12 V
6.5 A
e The battery is made from an arrangement of 10
identical cells as shown.
Calculate
i the emf of one cell
ii the internal resistance of one cell.
[1]
[2]
Paper 2, TZ1, May 2019, Q1
Determine the internal resistance of the battery. [2]
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B.5 Current and circuits
18
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C.1 Simple harmonic motion
Higher level
■ Paper 1
1 An object moves with simple harmonic motion. The
acceleration of the object is:
A constant
B always directed away from the centre of
the oscillation
C a maximum at the centre of the oscillation
D a maximum at the extremes of the oscillation.
Paper 1, November 2020, Q14
2 A particle performs simple harmonic motion. What is
the phase difference between the displacement and the
acceleration of the particle?
π
3π
C π
D
A 0
B
2
2
Paper 1, TZ1, May 2019, Q14
Ek
3 Which graph shows the variation with time t of the
kinetic energy of an object undergoing simple harmonic
motion (SHM) of period T?
A
1.5
1.0
0.5
B
Ek
0
–0.5
–1.0
–1.5
T
2T
t
0
–0.5
–1.0
T
2T
t
Ek
–1.5
1.5
1.0
0.5
Ek
0
D
B
C
v
2
2
3
D 3v
v
Q26 November 2019
5 A simple harmonic oscillator has a frequency f and
amplitude x0. If its phase angle is zero, its displacement
after time t is given by
A x0 cos (2πt/f )
B x0 cos (2πft)
C x0 sin (2πft)
D x0 sin (2πt/f )
6 An object undergoing simple harmonic motion (SHM)
has a period T and total energy E. The amplitude of
oscillations is halved. What are the new period and total
energy of the system?
Period
Total energy
A
T
2
E
4
B
T
2
E
2
C
T
E
4
D
T
E
2
1.5
1.0
0.5
C
4 An object undergoes simple harmonic motion of
amplitude x0. When the displacement of the object is
x0/3, the speed of the object is v. What is the speed when
the displacement is x0?
A 0
Paper 1, November 2018, Q26
T
2T
t
T
2T
t
1.5
1.0
0.5
0
Paper 1, TZ1, May 2019, Q15
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C.1 Simple harmonic motion
19
16/02/2023 20:33
1 A 2.0 kg mass is suspended vertically below a spring.
It is then made to oscillate. The spring constant
is 400 N m−1.
a Under what conditions would you expect that it
will undergo simple harmonic motion?
[1]
b Show that the frequency of simple harmonic
oscillations is approximately 2 Hz.
[3]
c Describe the energy changes that occur during one
cycle of the oscillation.
[3]
Higher level
2 The displacement, x, of a mass undergoing simple
harmonic motion is represented by the equation:
x = 0.024 sin (28t + ϕ)
a Explain the meaning of the symbol ϕ.
b Determine the time period of this oscillation.
c Calculate the displacement after 4.0 s if
i ϕ = 0
ii ϕ = π
d What is the maximum speed of the
oscillating mass?
[3]
[3]
[2]
[1]
[2]
■ Data-based question
When the rod is displaced by a small angle and then
released, simple harmonic oscillations take place in a
horizontal plane.
The theoretical oscillation for the period of oscillation T
is given by the following equation
c
T=
d g
where c is a known numerical constant.
a State the unit of c.
[1]
b A student records the time for 20 oscillations of
the rod. Explain how this procedure leads to a
more accurate measurement of the time for one
oscillation T.
[2]
c In one experiment d was varied. The graph shows
1
the plotted values of T against . Uncertainty bars
d
are negligibly small.
T/s
■ Paper 2
3.0
2.5
2.0
1.5
1.0
0.5
1 In an investigation to measure the acceleration of free
fall a rod is suspended horizontally by two vertical
strings of equal length. The strings are a distance d apart.
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
1/d/m–1
i
Draw the line of best fit for these data.
[1]
ii Suggest whether the data are consistent with the
theoretical prediction.
[2]
string
d The numerical value of the constant c in SI units
is 1.67. Determine g, using the graph.
[4]
string
d
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Paper 3, November 2018, Q1
rod
C.1 Simple harmonic motion
20
16/02/2023 20:33
C.2 Wave model
1 A transverse travelling wave is moving through a
medium. The graph shows, for one instant, the variation
with distance of the displacement of particles in
the medium.
Displacement
The frequency of the wave is 25 Hz and the speed of
the wave is 100 m s–1. Which statement is correct for
this wave?
up
0
Y
4 The graph shows the variation of the displacement of
a wave with distance along the wave. The wave speed
is 0.50 m s−1.
What is the period of the wave?
Wave displacement
■ Paper 1
Z
X
Distance
down
A The particles at X and Y are in phase.
B The velocity of the particle at X is a maximum.
C The horizontal distance between X and Z is 3.0 m.
D The velocity of the particle at Y is 100 m s–1.
Paper 1, November 2019, Q13
2 A sound wave has a frequency of 1.0 kHz and a
wavelength of 0.33 m. What is the distance travelled by
the wave in 2.0 ms and the nature of the wave?
Distance travelled in 2.0 ms
Nature of the wave
A
0.17 m
longitudinal
B
0.17 m
transverse
C
0.66 m
longitudinal
D
0.66 m
transverse
Paper 1, TZ1, May 2021, Q14
3 Which of the following is not a true statement about
electromagnetic waves?
A They all travel at the same speed through vacuum.
B Their frequency can be determined by multiplying
their speed by their wavelength.
C They are a combination of oscillating electric and
magnetic fields.
D They are transverse waves.
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0.0
0.75
1.50
2.25
3.0
Distance along wave/m
A 0.33 s
B 1.5 s
C 3.0 s
D 6.0 s
Paper 1, TZ2, May 2019, Q15
5 A longitudinal wave moves through a medium. Relative
to the direction of energy transfer through the medium,
what are the displacement of the medium and the
direction of propagation of the wave?
Displacement of the
medium
Direction of propagation
of wave
A
parallel
perpendicular
B
parallel
parallel
C
perpendicular
parallel
D
perpendicular
perpendicular
Paper 1, November 2018, Q12
C.2 Wave model
21
16/02/2023 20:33
■ Paper 2
6
Q
x/μm
4
2
0
P
0.2
0.4
0.6
–2
0.8
1.0
x/m
–4
–6
a i Calculate, in m s–1, the speed for this wave. [1]
ii Calculate, in Hz, the frequency for this wave. [2]
b The graph also shows the displacement of two
particles, P and Q, in the medium at t = 0.
State and explain which particle has the larger
magnitude of acceleration at t = 0.
[2]
Q3 (part) November 2019
8
6
4
2
0
–2
–4
–6
–8
1
2
3
4
5
6
t/ms
b Calculate the wavelength of the wave.
[2]
c Another wave travels in the medium. The graph
shows the variation with time t of the displacement
of each wave at the position of P.
x/μm
y/cm
1 The red line in the graph shows the variation with
distance x of the displacement y of a travelling wave at
t = 0. The blue line shows the wave 0.20 ms later. The
period of the wave is longer than 0.20 ms.
2 A longitudinal wave travels in a medium with speed
340 m s−1. The graph shows the variation with time t
of the displacement x of a particle P in the medium.
Positive displacements on the graph correspond to
displacements to the right for particle P.
a Describe how a longitudinal wave is different from
a transverse wave.
[2]
5
0
–5
0.5 1.0 1.5 2.0 2.5 3.0
t/ms
State the phase difference between the
two waves.
ii Identify a time at which the displacement of
P is zero.
i
[1]
[1]
Paper 2, November 2021, Q3 (part, adapted)
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C.2 Wave model
22
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C.3 Wave phenomena
■ Paper 1
1 In a double-slit experiment, a source of monochromatic
red light is incident on slits S1 and S2 separated by a
distance d. A screen is located at distance x from the slits.
A pattern with fringe spacing y is observed on the screen.
Three changes are possible for this arrangement:
I increasing x
II increasing d
III using green monochromatic light instead of red.
Which changes will cause a decrease in fringe spacing y?
slits
screen
S1
y
d
red monochromatic
source
S2
3 Three quantities used to describe a light wave are:
I frequency
II wavelength
III speed
Which quantities increase when the light wave passes
from water to air?
A I and II only
B I and III only
C II and III only
D I, II and III
Paper 1, TZ1, May 2021, Q16
Higher level
4 Light of frequency 500 THz is incident on a single slit
and forms a diffraction pattern. The first diffraction
minimum forms at an angle of 2.4 × 10 –3 rad to the
central maximum. The frequency of the light is now
changed to 750 THz. What is the angle between the first
diffraction minimum and the central maximum?
A 1.6 × 10 –3 rad
B 1.8 × 10 –3 rad
C 2.4 × 10 –3 rad
D 3.6 × 10 –3 rad
Paper 1, November 2019, Q27
5 Monochromatic light is incident on 4 rectangular,
parallel slits. The first principle maximum is observed at
angle θ to the direction of the incident light. The number
of slits is increased to 8 each having the same width and
spacing as the first 4.
x
A I and II only
B I and III only
C II and III only
D I, II, and III
Paper 1, November 2018, Q16
2 Two identical waves, each with amplitude X0 and
intensity I, interfere constructively. What are the
amplitude and intensity of the resultant wave?
Amplitude of the
resultant wave
Intensity of the
resultant wave
A
X0
2I
B
2X0
2I
C
X0
4I
D
2X0
4I
Paper 1, TZ1, May 2021, Q15
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Three statements about the first principal maximum
with 8 slits are
I
the angle at which it is observed is greater than θ
II its intensity increases
III its width decreases.
Which statements are correct?
A I and II only
B I and III only
C II and III only
D I, I and III
[1]
Paper 1, TZ1, May 2018, Q28
C.3 Wave phenomena
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6 White light is incident normally on separate diffraction
gratings X and Y. Y has a greater number of lines per
metre than X. Three statements about the differences
between X and Y are
I
adjacent slits in the gratings are further apart for
X than for Y
Higher level
2 Monochromatic light of wavelength 633 nm is normally
incident on a diffraction grating. The diffraction
maxima incident on a screen are detected and their
angle θ to the central beam is determined.
The graph shows the variation of sin θ with the order
n of the maximum. The central order corresponds to
n = 0.
II the angle between red and blue light in a spectral
order is greater in X than in Y
sin θ
III the total number of visible orders is greater for
X than for Y.
0.45
0.4
0.35
Which statements are correct?
0.3
A I and II only
0.25
B I and III only
0.2
C II and III only
0.15
D I, II and III
0.1
[1]
0.05
Paper 1, November 2020, Q29
0
0
■ Paper 2
1 A beam of microwaves is incident normally on a pair of
identical narrow slits S1 and S2.
When a microwave receiver is initially placed at W
which is equidistant from the slits, a maximum in
intensity is observed. The receiver is then moved
towards Z along a line parallel to the slits. Intensity
maxima are observed at X and Y with one minimum
between them. W, X and Y are consecutive maxima.
1
2
3
4
5
6
n
a Determine a mean value for the number of slits
per millimetre of the grating.
[4]
b State the effect on the graph of the variation of sin θ
with n of:
i using a light source with a smaller wavelength. [1]
ii increasing the distance between the diffraction
grating and the screen.
[1]
Paper 2, TZ2, May 2021, Q8 (part)
Not to scale
Z
1.181 m
microwave
transmitter
Y
X
S2
1.243 m
W
S1
a Explain why intensity maxima are observed at
X and Y.
[2]
The distance from S1 to Y is 1.243 m and the distance
from S2 to Y is 1.181 m.
b Determine the frequency of the microwaves.
[3]
c Outline one reason why the maxima observed at
W, X and Y will have different intensities from
each other.
[1]
Paper 2, TZ1, May 2019, Q3
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C.3 Wave phenomena
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C.4 Standing waves and resonance
■ Paper 1
1 The air in a pipe, open at both ends, vibrates in the
second harmonic mode.
What is the phase difference between the motion of a
particle at P and the motion of a particle at Q?
P
4 A student blows across the top of a cylinder that
contains water. A first-harmonic standing sound wave
is produced in the air of the cylinder. More water is
then added to the cylinder. The student blows so that
a first-harmonic standing wave is produced with a
different frequency.
What is the nature of the displacement in the air at the
water surface and the change in frequency when the
water is added?
Q
cylinder
A 0
B 2π
C π
D 2π
Paper 1, November 2020, Q17
2 A pipe is open at both ends. What is correct about a
standing wave formed in the air of the pipe?
A The sum of the number of nodes plus the number of
antinodes is an odd number.
B The sum of the number of nodes plus the number of
antinodes is an even number.
C There is always a central node.
D There is always a central antinode.
Paper 1, November 2019, Q16
3 The frequency of the first harmonic in a pipe is
measured. An adjustment is then made which causes the
speed of sound in the pipe to increase.
What is true for the frequency and the wavelength of the
first harmonic when the speed of sound has increased?
Frequency
Wavelength
A
increase
unchanged
B
unchanged
increase
C
increase
increase
D
unchanged
unchanged
Paper 1, TZ2, May 2021, Q17
water surface
Nature of displacement
Change in frequency
A
antinode
decrease
B
antinode
increase
C
node
decrease
D
node
increase
Paper 1, TZ2, May 2019, Q17
5 A string is fixed at both ends. P and Q are two particles
on the string.
The first-harmonic standing wave is formed in
the string.
What is correct about the motion of P and Q?
P
Q
A P is a node and Q is an antinode.
B P is an antinode and Q is a node.
C P and Q oscillate with the same amplitude.
D P and Q oscillate with the same frequency.
Paper 1, November 2021, Q17
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C.4 Standing waves and resonance
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■ Paper 2
1 One end of a string is attached to an oscillator and
the other is fixed to a wall. When the frequency of the
oscillator is 360 Hz the standing wave shown is formed
on the string.
Point X (not shown) is a point on the string at a distance
of 10 cm from the oscillator.
2 a Describe two ways in which standing waves differ
from travelling waves.
[2]
b A vertical tube, open at both ends, is completely
immersed in a container of water. A loudspeaker
above the container connected to a signal generator
emits sound. As the tube is raised the loudness of the
sound heard reaches a maximum because a standing
wave has formed in the tube.
2.10 m
signal generator
loudspeaker
oscillator
a State the number of all other points on the string that
have the same amplitude and phase as X.
[1]
b Determine the speed of the wave.
[2]
c The frequency of the oscillator is reduced to 120 Hz.
Draw the standing wave that will be formed on
the string.
[1]
water container
tube
Paper 2, November 2019, Q3 (adapted)
Outline how a standing wave forms in the tube.
[2]
ii The tube is raised until the loudness of the sound
reaches a maximum for a second time. Draw
the position of the nodes in the tube when the
second maximum is heard.
[1]
iii Between the first and second positions of
maximum loudness, the tube is raised through
0.37 m. The speed of sound in the air in the tube
is 320 m s−1. Determine the frequency of the
sound emitted by the loudspeaker.
[2]
i
Paper 2, TZ2, May 2021, Q5
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C.4 Standing waves and resonance
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■ Paper 1
D
1 The light from distant stars and galaxies is red-shifted.
This is because:
A the light is affected when it passes through the
Earth’s atmosphere.
B the stars and galaxies are moving apart from
each other.
C the spectra of light from stars and galaxies have
more red light than blue light.
D blue light in the spectra emitted by stars is absorbed
as it travels to Earth.
2 Light of wavelength 6.5 × 10−7 m is emitted by a star
moving away from Earth with a speed of 0.05c. The
wavelength detected on Earth will be:
A 3.3 × 10−8 m
B 6.8 × 10−7 m
C 6.2 × 10−7 m
D 6.5 × 10−7 m
3 On approaching a stationary observer, a train sounds
its horn and decelerates at a constant rate. At time t the
train passes by the observer and continues to decelerate
at the same rate.
Frequency measured
by observer
Which diagram shows the variation with time of the
frequency of the sound measured by the observer?
A
horn’s
frequency
Frequency measured
by observer
Time
t
Time
Paper 1, TZ1, May 2021, Q29
Higher level
4 An ambulance siren emits a sound of frequency
1200 Hz. The speed of sound in air is 330 m s–1. The
ambulance moves towards a stationary observer at a
constant speed of 40 m s–1.
What is the frequency heard by the observer?
A
B
C
D
1200 × 330
370
1200 × 290
330
1200 × 370
330
1200 × 330
290
Paper 1, November 2018, Q29
5 A train is moving in a straight line away from a
stationary observer when the train horn emits a sound of
frequency f0 . The speed of the train is 0.10 v where v is
the speed of sound.
A
horn’s
frequency
0.9
1.0
f0
B
( )
1.0
1.1
f0
C
( )
1.1
1.0
f0
D
( )
1.0
f
0.9 0
Paper 1, TZ2, May 2021, Q28
6 A train is approaching an observer with constant speed
c
Speed of Sound
Wavelength
A
c
33λ
34
B
35c
34
33λ
34
C
c
λ
D
35c
34
λ
horn’s
frequency
t
( )
34
where c is the speed of sound in still air. The train
emits sound of wavelength λ. What is the observed
speed of the sound and observed wavelength as the
train approaches?
Time
Frequency measured
by observer
t
C
horn’s
frequency
What is the frequency of the horn as heard by
the observer?
t
B
Frequency measured
by observer
C.5 Doppler effect
Time
Paper 1, TZ2, May 2018, Q27
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C.5 Doppler effect
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■ Paper 2
Higher level
1 Microwaves of wavelength 1.112 m are transmitted
from an aerial at an airport. The waves arrive at a
plane travelling directly towards the airport at a speed
of 250 m s−1.
a Calculate the frequency of the microwaves
(c = 3.00 × 108 m s−1)
[1]
b Explain why the plane receives the waves at a
slightly higher frequency than that with which they
were emitted.
[2]
c Show that the change in frequency is
approximately 200 Hz.
[2]
d What change of frequency is detected in the
reflected waves when they arrive back at
the airport?
[1]
3 Sound of frequency f = 2500 Hz is emitted from an
aircraft that moves with speed v = 280 m s–1 away from
a stationary observer. The speed of sound in still air
is 340 m s–1.
2 The lines on the spectra received from distant galaxies
all have lower frequencies than the light from the same
elements here on Earth.
a State the name scientists give to this effect.
[1]
b Explain why it occurs.
[3]
c Estimate the speed with which the distance between
Earth and a distant galaxy is increasing if a
wavelength emitted as 434 nm is received
as 456 nm.
[2]
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diagram not to scale
stationary
observer
a Calculate the frequency heard by the observer.
b What speed will the observer record for
i the sound waves
ii light waves
coming from the aircraft?
c Calculate the wavelength measured by
the observer.
[2]
[2]
[1]
Paper 2, TZ2, May 2019, Q3 (part, adapted)
C.5 Doppler effect
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D.1 Gravitational fields
Higher level
■ Paper 1
1 Two isolated point particles of mass 4M and 9M are
separated by a distance 1 m. A point particle of mass M
is placed a distance x from the particle of mass 9M. The
net gravitational force on M is zero.
What is x?
4M
M
9M
not to scale
4 A planet has radius R. The escape speed from the
surface of the planet is v. At what distance from the
surface of the planet is the orbital speed 0.5v?
A 0.5R
B R
C 2R
D 4R
Paper 1, TZ1, May 2021, Q32
x
5 A satellite orbits planet X with a speed vx at a distance
r from the centre of planet X. Another satellite orbits
planet Y at a speed of vY at a distance r from the centre
of planet Y. The mass of planet X is M and the mass of
planet Y is 4M. What is the ratio of vx : vY?
A 0.25
B 0.5
C 2.0
D 4.0
4
m
13
2
B m
5
3
C m
5
9
D
m
13
A
Paper 1, TZ2, May 2021, Q32
Paper 1, November 2018, Q23
2 Satellite X orbits a planet with orbital radius R. Satellite
Y orbits the same planet with orbital radius 2R.
Satellites X and Y have the same mass. What is the ratio
of centripetal acceleration of X : centripetal acceleration
of Y?
A ¼
B ½
C 2
D 4
Paper 1, TZ1, May 2019, Q25
3 Which graph shows the relationship between
gravitational force F between two point masses and
their separation r?
A
B
F
0
0
C
0
D
F
0
0
1
r
A
B
C
D
GMm
r
GMm
2r
GMm
4r
GMm
8r
Paper 1, November 2021, Q32
F
0
r2
6 A satellite of mass m orbits a planet of mass M in a
circular orbit of radius r. What is the work that must be
done on the satellite to increase its orbital radius to 2r?
r
F
0
0
1
r2
Paper 1, TZ2, May 2019, Q23
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D.1 Gravitational fields
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■ Paper 2
Higher level
1 A planet is in a circular orbit around a star. The speed of
the planet is constant.
a i Explain why a centripetal force is needed for the
planet to be in a circular orbit.
[2]
ii State the nature of this centripetal force.
[1]
b Determine the gravitational field of the planet.
The following data are given:
mass of planet = 8.0 × 1024 kg;
radius of planet = 9.1 × 106 m.
[2]
2 There is a proposal to place a satellite in orbit around the
planet Mars.
a i Outline what is meant by gravitational field
strength at a point.
[2]
ii Newton’s law of gravitation applies to point
masses. Suggest why the law can be applied to a
satellite orbiting Mars.
[2]
b The satellite is to have an orbital time T equal to the
length of a day on Mars. It can be shown that
T 2 = kR3 where R is the orbital radius of the satellite
and k is a constant.
i Mars has a mass of 6.4 × 1023 kg. Show that, for
Mars, k is about 9 × 10 –13 s2 m–3.
[3]
ii The time taken for Mars to revolve on its axis is
8.9 × 104 s. Calculate, in m s–1, the orbital speed of
the satellite.
[2]
Paper 2, TZ1, May 2021, Q2
Paper 2, November 2018, Q8
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D.1 Gravitational fields
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D.2 Electric and magnetic fields
Higher level
■ Paper 1
1 The Millikan oil drop experiment was evidence for the
quantization of charge. Which of the following is not a
possible value for the charge on an oil drop?
A 0.8 × 10−19 C
B 1.6 × 10−19 C
C 3.2 × 10−19 C
D 8.0 × 10−19 C
2 Magnetic field lines are an example of:
A a discovery that helps us understand magnetism.
B a model to aid in visualization.
C a pattern in data from experiments.
D a theory to explain concepts in magnetism.
4 Which is a correct unit for electric potential?
A J A–1 s−1
B JC
C J As−1
D J A−1 s
5 The diagram shows equipotential lines for an electric
field. Which arrow represents the acceleration of an
electron at point P?
100 V
200 V
300 V
A
Paper 1, TZ2, May 2021, Q22
D
3 Coulomb’s law can be expressed as F = kq1q2/r .
Which statement is correct?
P
B
2
C
A k is called the permittivity of free space.
B The equation cannot be applied to spherically
charged objects.
C If the distance between two charges is halved, the
force is doubled.
D The force between opposite charges has a
negative value.
Paper 1, November 2021, Q30
6 An electron is fixed in position in a uniform
electric field.
What is the position for which the electrical potential
energy of the electron is greatest?
A
D
e–
B
C
Paper 1, TZ2, May 2019, Q30
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D.2 Electric and magnetic fields
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■ Paper 2
Higher level
1 A vertical wall carries a uniform positive charge on its
surface. This produces a uniform horizontal electric
field perpendicular to the wall. A small, positively
charged ball is suspended in equilibrium from the
vertical wall by a thread of negligible mass.
2 The diagram shows the electric field lines of a positively
charged conducting sphere of radius R and charge Q.
wall
+
+
+
+
30°
+
+
+ +
+
+ + +
+
+
+
Q
E=
A
B
ball
a Explain why the electric potential decreases
from A to B.
[2]
b Draw, on a copy of the figure below, the variation
of electric potential V with distance r from the
centre of the sphere.
[2]
electric field
a The charge per unit area on the surface of the wall
is σ. It can be shown that the electric field strength E
due to the charge on the wall is given by the equation
σ
.
2ε0
Demonstrate that the units of the quantities in this
equation are consistent.
[2]
b i
Points A and B are located on the same field line.
The thread makes an angle of 30° with the
vertical wall. The ball has a mass of 0.025 kg.
Determine the horizontal force that acts on
the ball.
ii The charge on the ball is 1.2 × 10 C.
Determine σ.
[3]
–6
[2]
Paper 2, TZ2, May 2021, Q3
V
0
R
r
c A proton is placed at A and released from rest. The
magnitude of the work done by the electric field in
moving the proton from A to B is 1.7 × 10−16 J.
Point A is at a distance of 5.0 × 10−2 m from the
centre of the sphere.
Point B is at a distance of 1.0 × 10−1 m from the
centre of the sphere.
i Calculate the electric potential difference
between points A and B.
[1]
ii Determine the charge Q of the sphere.
[2]
d The concept of potential is also used in the context
of gravitational fields. Suggest why scientists
developed a common terminology to describe
different types of fields.
[1]
Paper 2, November 2020, Q8
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D.2 Electric and magnetic fields
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D.3 Motion in electromagnetic fields
■ Paper 1
1 A horizontal electrical cable carries a steady current out
of the page. The Earth’s magnetic field exerts a force on
the cable. Which arrow shows the direction of the force
on the cable due to the Earth’s magnetic field?
A
4 A current in a wire lies between the poles of a magnet.
What is the direction of the electromagnetic force on
the wire?
A
N
cable
D
B
B
S
C
current
Earth‘s surface
Paper 1, November 2020, Q19
D
C
Earth‘s magnetic field
Paper 1, TZ1, May 2019, Q19
5 A particle of mass m and charge of magnitude q enters a
region of uniform magnetic field B that is directed into
the page. The particle follows a circular path of radius R.
What is the sign of the charge of the particle, and the
speed of the particle?
2 An ion moves in a circle in a uniform magnetic field.
Which single change would increase the radius of the
circular path?
A Decreasing the speed of the ion
B Increasing the charge of the ion
C Increasing the mass of the ion
D Increasing the strength of the magnetic field
Paper 1, TZ2, May 2021, Q16
3 When a wire with an electric current I is placed in a
magnetic field of strength B it experiences a magnetic
force F. What is the direction of F?
A In a direction determined by I only
B In a direction determined by B only
C In the plane containing I and B
D At 90° to the plane containing I and B
Charge of the particle
A
positive
B
negative
C
negative
D
positive
Paper 1, November 2019, Q17
Speed of the particle
qBR
m
qBR
m
qBR
m
qBR
m
Paper 1, November 2018, Q19
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D.3 Motion in electromagnetic fields
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■ Paper 2
1 A proton is moving in a region of uniform magnetic
field. The magnetic field is directed into the plane of the
paper. The arrow shows the velocity of the proton at one
instant and the dotted circle gives the path followed by
the proton.
a Explain why the path of the proton is a circle.
[2]
6
–1
b The speed of the proton is 2.0 × 10 m s and the
magnetic field strength B is 0.35 T.
i Show that the radius of the path is about 6 cm. [2]
ii Calculate the time for one complete revolution. [2]
c Explain why the kinetic energy of the proton
is constant.
[2]
Paper 2, November 2019, Q4
proton
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2 Two long parallel wires, which are 50 cm apart, are
carrying currents of 2.0 A and 3.0 A in opposite
directions (in a vacuum).
a Explain why each wire experiences a force.
[2]
b What is the direction of the force on the wire
carrying 2 A?
[1]
c Calculate the force acting on each metre length of
the wire carrying a current of 3 A.
[2]
D.3 Motion in electromagnetic fields
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D.4 Induction (HL only)
■ Paper 1
1 The graph below shows the variation with time of the
magnetic flux through a coil.
Which of the following gives three times for which the
magnitude of the induced emf is a maximum?
4 The conservation of which quantity explains
Lenz’s law?
A Charge
B Energy
C Magnetic field
D Mass
Flux
Paper 1, TZ1, May 2021, Q34
5 A small magnet is released from rest to drop through a
stationary horizontal conducting ring.
0
What is the variation with time of the emf induced in
the ring?
Time
N
magnet
T
4
T
2
S
T
3T
4
A 0, T/4, T/2
B 0, T/2, T
C 0, T/4, T
D T/4, T/2, 3T/4
Paper 1, TZ1, May 2019, Q35
A
emf
Paper 1, November 2021, Q33
2 A circular coil of wire moves through a region of
uniform magnetic field directed out of the page.
Time
coil at position 1
coil at position 2
B
emf
What is the direction of the induced conventional
current in the coil for the marked positions?
Time
C
Position 2
A
clockwise
clockwise
B
anticlockwise
clockwise
C
clockwise
anticlockwise
D
anticlockwise
anticlockwise
Paper 1, TZ2, May 2019, Q29
3 A conducting ring encloses an area of 2.0 cm2 and is
perpendicular to a magnetic field of strength 5.0 mT. The
direction of the magnetic field is reversed in a time 4.0 s.
What is the average emf induced in the ring?
A 0
B 0.25 µV
C 0.40 µV
D 0.50 µV
Time
D
emf
Position 1
emf
direction
of motion
Time
Paper 1, TZ1, May 2021, Q33
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D.4 Induction (HL only)
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■ Paper 2
1 The diagram shows an alternating current generator
with a rectangular coil rotating at a constant frequency
in a uniform magnetic field.
2 A pendulum with a metal bob comes to rest after 200
swings. The same pendulum, released from the same
position, now swings at 90° to the direction of a strong
magnetic field and comes to rest after 20 swings.
sliding contacts
N
axis of rotation
S
V/kV
a Explain, by reference to Faraday’s law of induction,
how an electromotive force (emf) is induced in
the coil.
[3]
b The graph shows how the generator output voltage
V varies with time t.
100
75
a Explain why the pendulum comes to rest after a
smaller number of swings.
[4]
The magnet was rotated 180° and the experiment
was repeated.
b What difference will be observed (if any)?
Explain your answer.
[2]
Paper 2, TZ2, May 2021, Q7 (part, adapted)
50
25
0
–25
2
4
6
8
10
12
14
16
18 20
t/ms
–50
–75
–100
What is the frequency of the alternating
voltage?
[1]
ii The frequency at which the coil rotates is
doubled with no other changes being made.
Draw, on a copy of the graph, the variation with
time of the voltage output of the generator. [2]
i
Paper 2, November 2020, Q9 (adapted)
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E.1 Structure of the atom
Higher level
■ Paper 1
1 Which of the following atomic energy level transitions
corresponds to photons of the shortest wavelength?
A B C D
increasing
energy
4 Element X has a nucleon number AX and a nuclear
density ρX. Element Y has a nucleon number of 2AX.
What is an estimate of the nuclear density of element Y?
A ½ρX
B ρX
C 2ρX
D 8ρX
Paper 1, TZ2, May 2021, Q38
Paper 1, TZ1, May 2019, Q28
2 The Geiger–Marsden–Rutherford experiment
showed that:
A alpha particles cannot pass through thin gold foil.
B gold atoms contain a central uncharged nucleus.
C the positive charge in atoms is concentrated in a
small centre.
D electrons move in circular orbits.
3 Which of the following statements about energy levels
within atoms is not correct?
A The lowest energy level is called the ground state.
B A photon may be emitted when an electron moves to
a higher energy level.
C Values of energy levels can be determined from
measurements of spectral lines.
D All values of energy levels are considered to
be negative.
5 Three possible features of an atomic model are:
I orbital radius
II quantized energy
III quantized angular momentum.
Which of these are features of the Bohr model for
hydrogen?
A I and II only
B I and III only
C II and III only
D I, II, and III
Paper 1, TZ2, May 2019, Q39
6 When alpha particles approach nuclei in a very thin
sheet of gold, they are repelled, and their paths can
usually be predicted using Coulomb’s law. However,
Coulomb's law will not provide an accurate prediction if
A the gold is replaced with a less dense metal
B a beam of protons with less energy is used
C a thinner sheet of gold is used
D alpha particles of very high energy are used.
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■ Paper 2
Higher level
1 The diagram shows the position of the principal lines in
the visible spectrum of atomic hydrogen and some of the
corresponding energy levels of the hydrogen atom.
2 In a classical model of the singly-ionized helium atom,
a single electron orbits the nucleus in a circular orbit
of radius r.
electron
energy/10–19J
–0.605
–0.870
r
–1.36
–2.42
–5.44
helium nucleus
410 nm 488 nm
435 nm
656 nm
a Determine the energy of a photon of blue light
(435 nm) emitted in the hydrogen spectrum.
[3]
b Identify the transition in the hydrogen spectrum that
gives rise to the photon with the energy in part a.[1]
c Explain your answer to part b.[2]
Paper 2, November 2018, Q5
a Show that the speed v of the electron with mass m, is
given by:
2ke2
v=
[1]
mr
b Hence, deduce that the total energy of the electron is
given by:
ke2
Etotal = – [2]
r
c In this model the electron loses energy by emitting
electromagnetic waves. Describe the predicted
effect of this emission on the orbital radius of
the electron.
[2]
Paper 2, November 2019, Q8 (part)
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E.2 Quantum physics (HL only)
■ Paper 1
■ Paper 2
1 Photons of a certain frequency incident on a metal
surface cause the emission of electrons from the surface.
The intensity of the light is constant and the frequency
of photons is increased.
1 In an electric circuit used to investigate the photoelectric
effect, the voltage is varied until the reading in the
ammeter is zero. The stopping voltage that produces this
reading is 1.40 V.
What is the effect, if any, on the number of emitted
electrons and the energy of emitted electrons?
Number of emitted
electrons
Energy of emitted
electrons
A
No change
No change
B
Decrease
Increase
C
Decrease
No change
D
No change
Increase
beam of light
e–
A
Paper 1, TZ2, May 2019, Q38
2 On which one of the following factors does the Compton
scattering shift depend?
A Amplitude of incident radiation
B Wavelength of incident radiation
C Angle of scattering
D Chemical nature of scattering substance
3 When green light is incident on a clean zinc plate no
photoelectrons are emitted. What change may cause the
emission of photoelectrons?
A Using a metal plate with larger work function.
B Changing the angle of incidence of the green light on
the zinc plate.
C Using shorter wavelength radiation.
D Increasing the intensity of the green light.
Paper 1, November 2018, Q37
4 A beam of monochromatic radiation is made up of
photons each of momentum p. The intensity of the beam
is doubled without changing frequency. What is the
momentum of each photon after the change?
A p/2
B p
C 2p
D 4p
V
a Describe the photoelectric effect.
[2]
b Show that the maximum velocity of the
photoelectrons is 700 km s−1.[2]
c The photoelectrons are emitted from a sodium
surface. Sodium has a work function of 2.3 eV.
Calculate the wavelength of the radiation incident
on the sodium. State an appropriate unit for
your answer.
[3]
Paper 2, TZ1, May 2021, Q10
2 A beam of electrons is produced by accelerating the
particles from rest across a vacuum by a potential
difference of 3.4 × 105 V.
a Calculate the maximum momenta of the electrons. [3]
b Use de Broglie’s hypothesis to predict the
wavelength of the electrons.
[2]
c Electrons are believed to exist as standing waves
within electrons. Describe how Bohr’s model of the
atom is different from this theory.
[2]
Paper 1, November 2019, Q38
5 Electrons accelerated by a potential difference across a
vacuum can be made to diffract through a crystalline
structure. The potential difference is then increased.
Which of the following is not true about the electrons?
A They will gain a greater speed.
B They will diffract through a larger angle.
C They will have a smaller wavelength.
D They will gain a greater momentum.
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E.3 Radioactive decay
■ Paper 1
1 Three particles are produced when the nuclide 23
12 Mg
undergoes beta-plus (β+) decay. What are two of
these particles?
0
A 23
11 Na and 0 v
B –10 e and 00 v
0
C 23
11 Na and 
0v
0
0
D 1 e and 0 v
Paper 1, TZ2, May 2021, Q26
2 When a high-energy α-particle collides with a
beryllium-9 (94Be) nucleus, a nucleus of carbon
(Z = 6) may be produced. What are the products of
this reaction?
Product 1
Product 2
A
carbon-12
proton
B
carbon-12
neutron
C
carbon-14
proton
D
carbon-14
neutron
Paper 1, TZ2, May 2021, Q25
3 X is a radioactive nuclide that decays to a stable nuclide.
The activity of X falls to 1⁄16th of its original value
in 32 s. What is the half-life of X?
A 2s
B 4s
C 8s
D 16 s
Paper 1, November 2019, Q26
Higher level
4 The half-life of a radioactive nuclide is 8.0 s. The initial
activity of a pure sample of the nuclide is 10 000 Bq.
What is the approximate activity of the sample
after 4.0 s?
A 2500 Bq
B 5000 Bq
C 7100 Bq
D 7500 Bq
Paper 1, TZ1, May 2019, Q39
5 What was a reason to postulate the existence
of neutrinos?
A Nuclear energy levels had a continuous spectrum.
B The photon emission spectrum only contained
specific wavelengths.
C Some particles were indistinguishable from
their antiparticle.
D The energy of emitted beta particles had a
continuous spectrum.
6 A radioactive nuclide is known to have a very long halflife. Three quantities known for a pure sample of the
nuclide are:
I the activity of the nuclide
II the number of nuclide atoms
III the mass number of the nuclide.
What quantities are required to determine the half-life
of the nuclide?
A I and II only
B I and III only
C II and III only
D I, II and III
Paper 1, November 2018, Q40
■ Paper 2
1 a Radioactive decay is said to be ‘random’ and
‘spontaneous’. Outline what is meant by each of
these terms.
[2]
b A stationary nucleus of uranium-238 undergoes
alpha decay to form thorium-234. The following data
are available.
Energy released in decay 4.27 MeV
Binding energy per nucleon for helium 7.07 MeV
Binding energy per nucleon for thorium 7.60 MeV
i Calculate the binding energy per nucleon for
uranium-238.[3]
ii Calculate the ratio:
kinetic energy of alpha particle : kinetic energy
of thorium nucleus
[2]
Paper 2, November 2019, Q7
Higher level
32
15
P undergoes beta-minus (β–) decay. Explain why
the energy gained by the emitted beta particles in
this decay is not the same for every beta particle.[2]
b i State what is meant by decay constant.
[2]
ii In a fresh pure sample of 32
P
the
activity
of
the
15
sample is 24 Bq. After one week the activity
has become 17 Bq.
Calculate, in s–1, the decay constant of 32
15 P.[3]
2 a
Paper 2, November 2018, Q6 (part)
Paper 1, TZ1, May 2021, Q40
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E.4 Fission
■ Paper 1
1 A neutron collides head-on with a stationary atom in
the moderator of a nuclear power station. The kinetic
energy of the neutron changes as a result. There is also
a change in the probability that this neutron can cause
nuclear fission.
nuclear energy
in fuel
thermal energy
in steam
electrical energy
thermal energy loss
in turbine
thermal energy loss
in heat exchanger
What are these changes?
Change in kinetic energy
of the neutron
Change in probability of
causing nuclear fission
A
increase
increase
B
decrease
increase
C
increase
decrease
D
decrease
decrease
Paper 1, TZ2, May 2019, Q36
2 The mass of nuclear fuel in a nuclear reactor decreases
at the rate of 8 mg every hour. The overall reaction
process has an efficiency of 50%.
What is the maximum power output of the reactor?
A 100 MW
B 200 MW
C 100 GW
D 200 GW
Paper 1, November 2020, Q24
3 What is the function of control rods in a nuclear
power plant?
A To slow neutrons down
B To regulate fuel supply
C To exchange thermal energy
D To regulate the reaction rate
Paper 1, November 2018, Q23
4 A nuclear power station contains an alternating
current generator.
What energy transfer is performed by the generator?
A Electrical to kinetic
B Kinetic to electrical
C Nuclear to kinetic
D Nuclear to electrical
Paper 1, November 2020, Q25
5 The Sankey diagram shows the energy transfers in a
nuclear power station.
Electrical power output of the power station is 1000 MW.
What is the thermal power loss in the heat exchanger?
A 500 MW
B 1000 MW
C 1500 MW
D 2500 MW
Paper 1, November 2021, Q29
■ Paper 2
1 a Describe the nature of high-level nuclear waste
materials from a nuclear power station.
[2]
b Explain why the disposal of nuclear waste is
considered to be a long-term problem.
[1]
c Name two methods for the long-term storage of
nuclear waste.
[2]
2 a One possible fission reaction of uranium-235
(U-235) is:
235
1
140
94
1
92 U + 0 n → 54 Xe + 38 Sr + 2 0 n
The following data are available:
Mass of one atom of U-235 = 235 u
Binding energy per nucleon for U-235 = 7.59 MeV
Binding energy per nucleon for Xe-140 = 8.29 MeV
Binding energy per nucleon for Sr-94 = 8.59 MeV
i State what is meant by binding energy of
a nucleus.[1]
ii Outline why quantities such as atomic mass and
nuclear binding energy are often expressed in
non-SI units.
[1]
iii Show that the energy released in the reaction is
about 180 MeV.
[1]
b A nuclear power station uses U-235 as fuel. Assume
that every fission reaction of U-235 gives rise to
180 MeV of energy.
i Estimate, in J kg–1, the specific energy (energy
from unit mass) of U-235.
[2]
ii The power station has a useful power output of
1.2 GW and an efficiency of 36%.
Determine the mass of U-235 that undergoes
fission in one day.
[2]
iii The specific energy of fossil fuel is typically
30 MJ kg–1.
Suggest, with reference to your answer to part b,
one advantage of U-235 compared with fossil
fuels in a power station.
[1]
Paper 2, November 2020, Q6 (part)
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E.5 Fusion and stars
■ Paper 1
■ Paper 2
1 Two nuclei of low mass fuse together to make one larger
nucleus. In this reaction:
A the total mass after the fusion is greater than before.
B the total binding energy has decreased.
C there is an overall release of energy.
D the nuclei cannot fuse unless they are moving slowly.
1 a Suggest the conditions that will cause the Sun to
become a red giant.
[3]
b Outline why the Sun will maintain a constant
radius after it becomes a white dwarf.
[1]
c During its evolution, the Sun is likely to be a red
giant of surface temperature 3000 K and luminosity
104 L⊙. Later it is likely to be a white dwarf of surface
temperature 10 000 K and luminosity 10−4 L⊙.
Calculate the radius of the Sun as a white dwarf /
radius of the Sun as a red giant.
[2]
3 A and B are two main sequence stars. Star A has a
radius one hundred times greater than star B.
Which of the following is not a true statement about
star A, compared to star B?
A Star A has greater surface temperature.
B Star A has a greater luminosity.
C Star A is redder in colour.
D Star A has a greater mass.
4 More massive main sequence stars have shorter
lifetimes (than less massive stars) because:
A they have a much greater rate of fusion.
B they contain less hydrogen.
C they have a lower core temperature.
D they have a lower luminosity.
5 What is the distance from Earth to a star if it has a
parallax angle of 0.2 arc-seconds?
A 0.2 pc
B 0.4 pc
C 5 pc
D 10 pc
Paper 3, TZ2, May 2019, Q15 (part)
2 The Hertzsprung–Russell (HR) diagram shows the Sun
and a main sequence star X.
The luminosity of star X is 280 times greater than the
luminosity of the Sun L⊙.
Luminosity
2 A main sequence star can remain in equilibrium because:
A the inwards radiation pressure balances the outwards
nuclear forces.
B the outwards radiation pressure balances the inwards
nuclear forces.
C the inwards radiation pressure balances the outwards
gravitational forces.
D the outward radiation pressure balances the inwards
gravitational forces.
X
L.
Sun
Temperature
a If the radius of Star X is 3.2 times the radius of the
Sun, determine the ratio of surface temperature of
star X : surface temperature of the Sun.
[2]
b The parallax angle for star X is 0.125 arc-second.
i Outline how the parallax angle of a star can
be measured.
[2]
ii Show that the distance to star X is 1.6 × 106 AU.[2]
iii The apparent brightness of the Sun is
1400 W m–2.
Calculate, in W m–2, the apparent brightness
of star X.
[2]
c Star X will evolve to become a white dwarf star.
Describe where white dwarf stars are located on
the HR diagram.
[1]
Paper 3, TZ1, May 2019, Q17 (part)
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