1 Momentum
Intermediate level
1 Define linear momentum and state its SI unit.
[2]
2 A bumper-car collides at right-angles with a metal barrier and rebounds at the same speed.
A student suggests that the change in momentum of the car is zero.
Explain why the student is wrong.
[2]
3 Each diagram shows a 2.0 kg object before and after a collision.
Calculate the change in momentum of the object in each case.
a
[2]
b
[2]
c
[2]
4 Which of the following objects has greater momentum?
• A 10-tonne lorry travelling at a velocity of 20 m s−1.
• A 1.5 g dust particle hurtling through space at a velocity of 20 km s−1.
5 A 0.200 kg metal ball is dropped from a height of 1.5 m above the ground.
a Show that the speed of the ball just before it hits the ground is about 5.4 m s−1.
(The acceleration of free fall is 9.81 m s−2.)
b The ball bounces from ground with half of its impact speed.
Calculate the size of the change in momentum of the ball.
[3]
[3]
[2]
Higher level
6 A cannon of mass 850 kg fires a 20 kg shell at a velocity of 180 m s−1.
a Calculate the final momentum of the shell.
b What is the magnitude of the momentum of the cannon immediately after the shell
is fired? (You may assume that the cannon is initially at rest.)
c Calculate the recoil velocity V of the cannon.
[2]
[2]
[3]
7 A car of mass 900 kg travelling at a velocity of 28 m s−1 makes a head-on collision with a stationary van of mass
1500 kg. The car and the van get tangled together.
a Calculate the combined speed of the tangled vehicles immediately after the collision.
[4]
b Calculate the initial kinetic energy of the car and the final kinetic energy of the tangled
car and van immediately after the collision.
[3]
c Use your answer to b to explain whether the collision is elastic or inelastic.
[1]
8 The diagram below shows the initial state of two trolleys A and B before colliding and the
final state immediately after the collision.
1
Calculate the final velocity v of trolley B.
[4]
9 A bullet of mass 30 g is fired at a speed of 140 m s−1 into a stationary block of wood of mass
460 g. The bullet becomes embedded into the wood.
a Calculate the common speed of the block of wood and the bullet after the impact.
b Calculate the initial kinetic energy of the bullet and the final kinetic energy of the block
of wood and the embedded bullet.
c Use your answers to b to suggest whether the collision between the bullet and the block
of wood is elastic or inelastic.
[4]
[3]
[1]
Extension
10 A stationary radioactive nucleus of mass M ejects an -particle of mass m at a speed of
2.0 × 107 m s−1. Given M = 55m, calculate the kinetic energy of the -particle as a percentage
of the final total kinetic energy.
[6]
11 The diagram below shows the initial state of two identical balls A and B before collision and
the final state immediately after the collision.
The mass of each ball is 1.2 kg.
Before the collision, the velocity of A is 3.0 m s−1 and B is stationary.
A makes an oblique collision with B.
After the collision, A moves off at an angle of 30° to its original direction and has a velocity
of 2.6 m s−1. B is deflected at an angle  with a velocity of 1.5 m s−1.
a Explain why the final momentum of the system in a direction at right angles to the initial
velocity of A is zero. Hence determine the angle .
b Show that the total momentum of the system is conserved.
Total:
57
Score:
[3]
[3]
%
2
2 Momentum and Newton’s laws
Intermediate level
1 Write a word equation for Newton’s second law.
[1]
2 A car of mass 800 kg starts from rest. After 12 s, its velocity is 20 m s−1.
Calculate the average force acting on the car.
[3]
3 The diagram below shows two isolated charged particles X and Y repelling each other.
The mass of X is 6.6 × 10−27 kg and the mass of Y is 1.7 × 10−27 kg.
At a particular instant, the force on X is 0.20 N.
a State the magnitude of the force F on Y.
b State and explain which of these two particles will have a greater acceleration.
c Determine the acceleration of particle Y.
4 a Define the impulse of a force.
b State the relationship between the impulse of a force and the change in the momentum of
the object.
c Using the base units:
kilogram (kg), metre (m) and second (s)
show that impulse has the same unit as momentum.
[1]
[2]
[2]
[1]
[1]
[3]
5 A constant force of 12 N acts on a ball of mass 0.050 kg for a time of 0.030 s.
a Calculate the impulse of the force.
b The ball was initially at rest. Calculate its final velocity.
[2]
[3]
6 A 0.30 g fly moving at 1.5 m s−1 is trapped by a spider’s web.
The fly comes to rest in a time of 0.40 s. Calculate the magnitude of:
a the change in momentum of the fly
b the average force exerted by the web on the fly.
[2]
[3]
Higher level
7 The diagram shows two toy trains T
and R held in place on a level track
against the force exerted by a
compressed spring.
When the trains are released,
R moves to the right at a speed
of 3.8 m s−1. The spring takes 0.25 s
to uncoil to its natural length.
a Calculate the velocity of train T.
b Calculate the average force exerted by the spring on each train.
8 A ball of mass 210 g moving at a speed of 23 m s−1 hits a wall at right-angles and rebounds
at the same speed. The ball is in contact with the wall for 0.31 s.
a Calculate the change in momentum of the ball.
[4]
[4]
[2]
3
b Is the momentum of the ball conserved? Explain your answer.
c Calculate the magnitude of the average force acting on the ball.
[2]
[3]
9 A 900 kg car crashes into a safety barrier. The diagram below show how the force F acting
on the car changes with time t while the car is being stopped.
The final velocity of the car is zero.
a Use the graph above to determine the impulse of the force.
b Calculate the initial velocity of the car.
[3]
[3]
Extension
10 A hose ejects water at a velocity of 3.0 m s−1 through a hole of cross-sectional area
1.2 × 10−4 m2. The water strikes a wall normally; its final velocity is zero.
Calculate the force acting on the wall due to the impact of the water.
The density of water is 1000 kg m−3.
[5]
11 The diagram shows flour falling onto a horizontally moving conveyor belt.
The flour falls vertically onto the conveyor belt at a constant rate of 3.2 kg s−1.
The conveyor belt is moving at a constant speed of 1.5 m s−1.
Calculate the extra horizontal force required to keep the belt moving at its constant speed.
Total:
54
Score:
[4]
%
4
3 Circular motion
acceleration of free fall g = 9.81 m s−2
Intermediate level
1 Convert the following angles into radians.
a 30°
b 210°
c 0.05°
[1]
[1]
[1]
2 Convert the following angles from radians into degrees.
a 1.0 rad
b 4.0 rad
c 0.15 rad
[1]
[1]
[1]
3 The planet Mercury takes 88 days to orbit once round the Sun.
Calculate its angular displacement in radians during a time interval of:
a 44 days
b 1 day.
[1]
[1]
4 In each case below, state what provides the centripetal force on the object.
a A car travels at a high speed round a sharp corner.
b A planet orbits the Sun.
c An electron orbits the positive nucleus of an atom.
d Clothes spin round in the drum of a washing machine.
[1]
[1]
[1]
[1]
5 An aeroplane is circling in the sky at a speed of 150 m s–1.
The aeroplane describes a circle of radius 20 km.
For a passenger of mass 80 kg inside this aeroplane, calculate:
a her centripetal acceleration
b the centripetal force acting on her.
[3]
[2]
6 The diagram shows a stone tied to the end of a length of string.
It is whirled round in a horizontal circle of radius 80 cm.
The stone has a mass of 90 g and it completes 10 revolutions in a time of 8.2 s.
a Calculate:
This distance is
i
the time taken for one revolution
equal to the
circumference of the
ii the distance travelled by the stone during one revolution
circle.
iii the speed of the stone as it travels in the circle
iv the centripetal acceleration of the stone
v the centripetal force on the stone.
b What provides the centripetal force on the stone?
c What is the angle between the acceleration of the stone and its velocity?
[1]
[1]
[2]
[3]
[2]
[1]
[1]
5
Higher level
7 A lump of clay of mass 300 g is placed
close to the edge of a spinning turntable.
The centre of mass of the lump of clay travels
in a circle of radius 12 cm.
a
The lump of clay takes 1.6 s to complete one revolution.
i Calculate the rotational speed of the clay.
ii Calculate the frictional force between the clay and the turntable.
b The maximum magnitude of the frictional force F between the clay and the turntable is
70% of the weight of the clay. The speed of rotation of clay is slowly increased.
Determine the speed of the clay when it just starts to slip off the turntable.
[2]
[3]
[4]
8 The diagram shows a skateboarder of mass 70 kg who drops through a vertical height
of 5.2 m.
The dip has a radius of curvature of 16 m.
a Assuming no energy losses due to air resistance or friction, calculate the speed of the skateboarder at the
bottom of the dip at point B.
You may assume that the speed of the skateboarder at point A is zero.
[2]
b i Calculate the centripetal acceleration of the skateboarder at point B.
[3]
ii Calculate the contact force R acting on the skateboarder at point B.
[3]
Extension
9 A car of mass 820 kg travels at a constant speed
of 32 m s–1 along a banked track.
The track is banked at an angle of 20°
to the horizontal.
a
The net vertical force on the car is zero.
Use this to show that the contact force R on the car is 8.56 kN.
b Use the answer from a to calculate the radius of the circle described by the car.
[2]
[4]
10 A stone of mass 120 g is fixed to one end of a light rigid rod.
6
The stone is whirled at a constant speed of 4.0 m s–1 in a vertical circle of radius 80 cm.
tension in the rod at A
Calculate the ratio:
tension in the rod at B
Total:
57
Score:
[6]
%
7
4 Gravitational fields
gravitational constant G = 6.67 × 10–11 N m2 kg–2
Intermediate level
1 Define gravitational field strength at a point in space.
[1]
2 Show that the gravitational constant G has the unit N m2 kg–2.
[2]
3 The gravitational field strength on the surface of the Moon is 1.6 N kg–1.
What is the weight of an astronaut of mass 80 kg standing on the surface of the Moon?
[2]
4 Calculate the magnitude of the gravitational force between the objects described below.
You may assume that the objects are ‘point masses’.
a two protons separated by a distance of 5.0 × 10–14 m
(mass of a proton = 1.7 × 10–27 kg)
[3]
b two binary stars, each of mass 5.0 × 1028 kg, with
a separation of 8.0 × 1012m
[2]
c
[2]
two 1500 kg elephants separated by a distance of 2.0 m
5 The diagram shows the Moon and an artificial satellite orbiting round the Earth.
The radius of the Earth is R.
a
Write an equation for the gravitational field strength g at a distance r from the centre of
an isolated object of mass M.
b By what factor would the gravitational field decrease if the distance from the centre of
the mass were doubled?
c The satellite orbits at a distance of 5R from the Earth’s centre and the Moon is at a
distance of 59R. Calculate the ratio:
gravitatio nal field strength at position of satellite
gravitatio nal field strength at position of Moon
[1]
[2]
[3]
Higher level
6 The planet Neptune has a mass of 1.0 × 1026 kg and a radius of 2.2 × 107 m.
Calculate the surface gravitational field strength of Neptune.
[3]
8
7 Calculate the radius of Pluto, given its mass is 5.0 × 1023 kg and its surface
gravitational field strength has been estimated to be 4.0 N kg–1.
[3]
8 A space probe of mass 1800 kg is travelling from Earth to the planet Mars.
The space probe is midway between the planets. Use the data given to calculate:
a the gravitational force on the space probe due to the Earth
b the gravitational force on the space probe due to Mars
c the acceleration of the probe due to the gravitational force acting on it.
[3]
[2]
[3]
Data
separation between Earth and Mars = 7.8 × 1010 m
mass of Earth = 6.0 × 1024 kg
mass of Mars = 6.4 × 1023 kg
9 An artificial satellite orbits the Earth at a height of 400 km above its surface.
The satellite has a mass 5000 kg, the radius of the Earth is 6400 km and the mass of the
Earth is 6.0 × 1024 kg. For this satellite, calculate:
a the gravitational force experienced
b its centripetal acceleration
c its orbital speed.
10 a State Kepler’s third law of planetary motion.
b The Moon orbits the Earth at a distance of 3.84 × 105 km from the centre of the Earth.
The orbital period of the Moon is 27.3 days. Use this information to calculate:
i the distance from the Earth’s centre of a geostationary satellite
ii the mass of the Earth.
[3]
[2]
[3]
[1]
[3]
[3]
Extension
11 The planets in our Solar System orbit the Sun in almost circular orbits.
a Show that the orbital speed v of a planet at a distance r from the centre of the Sun is
given by:
GM
v=
r
b The mean distance between the Sun and the Earth is 1.5 × 1011 m and the mass of the Sun
is 2.0 × 1030 kg.
Calculate the orbital speed of the Earth as it travels round the Sun.
[4]
[2]
12 There is point between the Earth and the Moon where the net gravitational field strength
is zero. At this point the Earth’s gravitational field strength is equal in magnitude but
opposite in direction to the gravitational field strength of the Moon.
Given that:
mass of Earth
= 81
mass of Moon
calculate how far this point is from the centre of the Moon in terms of R, where R is
the separation between the centres of the Earth and the Moon.
Total:
57
Score:
[4]
%
9
5 Oscillations
Intermediate level
1 For an oscillating mass, define:
a the period
b the frequency.
[1]
[1]
2 The graph of displacement x against time t for an object executing simple harmonic motion
(s.h.m.) is shown here.
a State a time at which the object has maximum speed. Explain your answer.
b State a time at which the magnitude of the object’s acceleration is a maximum.
Explain your answer.
[2]
[2]
3 An apple is hung vertically from a length of string to form a simple pendulum.
The apple is pulled to one side and then released. It executes 12 oscillations in a time of 13.2 s.
a Calculate the period of the oscillations.
[2]
b Calculate the frequency of the oscillations.
[2]
4 This is the graph of displacement x against time t graph for an oscillating object.
Use the graph to determine the following:
a the amplitude of the oscillation
b the period
c the frequency in hertz (Hz)
d the angular frequency in radians per second (rad s–1).
e the maximum speed of the oscillating mass.
[1]
[1]
[2]
[2]
[2]
10
5 Two objects A and B have the same period of oscillation. In each case a and b below,
determine the phase difference between the motions of the objects A and B.
a
b
6 A mass at the end of a spring oscillates with a period of 2.8 s.
The maximum displacement of the mass from its equilibrium position is 16 cm.
a What is the amplitude of the oscillations?
b Calculate the angular frequency of the oscillations.
c Determine the maximum acceleration of the mass.
d Determine the maximum speed of the mass.
[2]
[2]
[1]
[2]
[3]
[2]
Higher level
7 A small toy boat is floating on the water’s surface. It is gently pushed down and then
released. The toy executes simple harmonic motion. Its displacement against time graph
is shown here.
For this oscillating toy boat, calculate:
a its angular frequency
b its maximum acceleration
c its displacement after a time of 6.7 s, assuming that the effect of damping on the boat is
negligible.
[2]
[3]
[3]
11
8 The diagram shows the displacement against time graph for a particle executing simple
harmonic motion.
Sketch the following graphs for the oscillating particle:
a velocity against time graph
b acceleration against time graph
c kinetic energy against time graph
d potential energy against time graph.
[2]
[2]
[2]
[2]
9 A piston in a car engine executes simple harmonic motion.
The acceleration a of the piston is related to its displacement x by the equation:
a = –6.4 × 105x
a Calculate the frequency of the motion.
b The piston has a mass of 700 g and a maximum displacement of 8.0 cm.
Calculate the maximum force on the piston.
[3]
[2]
Extension
10 The diagram shows a trolley of mass m attached
to a spring of force constant k. When the trolley
is displaced to one side and then released, the
trolley executes simple harmonic motion.
a
Show that the acceleration a of the trolley is given by the expression:
k
a =   x
m
where x is the displacement of the trolley from its equilibrium position.
b Use the expression in a to show that the frequency f of the motion is given by:
1 k
f=
2 m
c The springs in a car’s suspension act in a similar way to the springs on the trolley.
For a car of mass 850kg, the natural frequency of oscillation is 0.40 s.
Determine the force constant k of the car’s suspension.
Total:
59
Score:
[3]
[2]
[3]
%
12
6 Thermal physics
specific heat capacity of water = 4200 J kg–1 K–1
Intermediate level
1 Describe the arrangement of atoms, the forces between the atoms and the motion of the
atoms in:
a a solid
b a liquid
c a gas.
[3]
[3]
[3]
2 A small amount of gas is trapped inside a container. Describe the motion of the gas atoms
as the temperature of the gas within the container in increased.
[3]
3 a Define the internal energy of a substance.
b The temperature of an aluminium block increases when it is placed in the flame of a
Bunsen burner. Explain why this causes an increase in its internal energy.
c
A lump of metal is melting in a hot oven at a temperature of 600 °C.
Explain whether its internal energy is increasing or decreasing as it melts.
[1]
[3]
[4]
4 Write a word equation for the change in the thermal energy of a substance in terms of its
mass, the specific heat capacity of the substance and its change of temperature.
[1]
5 During a hot summer’s day, the temperature of 6.0 × 105 kg of water in a swimming pool
increases from 21 °C to 24 °C. Calculate the change in the internal energy of the water.
[3]
6 A 300 g block of iron cools from 300 °C to room temperature at 20 °C. The specific heat
capacity of iron is 490 J kg–1 K–1. Calculate the heat released by the block of iron.
[3]
13
Higher level
7 a
Change the following temperatures from degrees Celsius into kelvin.
i 0 °C
ii 80 °C
iii –120 °C
b Change the following temperatures from kelvin into degrees Celsius.
i 400 K
ii 272 K
iii 3 K
8 An electrical heater is used to heat 100 g of water in a well-insulated container at a steady
rate. The temperature of the water increases by 15 °C when the heater is operated for a
period of 5.0 minutes. Determine the change of temperature of the water when the same
heater and container are individually used to heat:
a 300 g of water for the same period of time
b 100 g of water for a time of 2.5 minutes.
[3]
[3]
[3]
[3]
9 The diagram below shows the variation of the temperature of 200 g of lead as it is heated
at a steady rate.
a Use the graph to state the melting point of lead.
b Explain why the graph is a straight line at the start.
c Explain what happens to the energy supplied to the lead as it melts at a constant
temperature.
d The initial temperature of the lead is 0 °C. Use the graph to determine the total
energy supplied to the lead before it starts to melts.
(The specific heat capacity of lead is 130 J kg–1 K–1.)
e Use your answer to d to determine the rate of heating of the lead.
[1]
[1]
[1]
[3]
[2]
10 The diagram shows piped water being heated by an electrical heater.
The water flows through the heater at a rate of 0.015 kg s–1. The heater warms the water
from 15 °C to 42 °C. Assuming that all the energy from the heater is transferred to
heating the water, calculate the power of the heater.
[5]
14
Extension
11 Hot water of mass 300 g and at a temperature of 90 °C is added to 200 g of cold water
at 10 °C. What is the final temperature of the mixture? You may assume there are no
losses to the environment and all heat transfer takes place between the hot water and
the cold water.
[5]
12 A metal cube of mass 75 g is heated in a naked flame until it is red hot. The metal block is
quickly transferred to 200 g of cold water. The water is well stirred. The graph shows the
variation of the temperature of the water recorded by a datalogger during the experiment.
The metal has a specific heat capacity of 500 J kg–1 K–1. Use the additional information
provided in the graph to determine the initial temperature of the metal cube. You may
assume there are no losses to the environment and all heat transfer takes place between
the metal block and the water.
Total:
62
Score:
[5]
%
15
7 Ideal gases
Boltzmann constant k = 1.38 × 1023 J K1
Avogadro constant NA = 6.02 × 1023 mol–1
universal gas constant R = 8.31 J mol–1 K–1
Intermediate level
1 Determine the number of atoms or molecules in each of the following.
a 1.0 mole of carbon
b 3.6 moles of water
c 0.26 moles of helium
[1]
[1]
[1]
2 The molar mass of helium is 4.0 g.
Determine the mass of a single atom of helium in kilograms.
[2]
3 The molar mass of uranium is 238 g.
a Calculate the mass of one atom of uranium.
b A small rock contains 0.12 g of uranium. For this rock, calculate the number of:
i moles of uranium
ii atoms of uranium.
[2]
[2]
[1]
4 Explain what is meant by the absolute zero of temperature.
[3]
5 a Write the ideal gas equation in words.
b One mole of an ideal gas is trapped inside a rigid container of volume 0.020 m3.
What pressure is exerted by the gas when the temperature within the container is 293 K?
[1]
[3]
Higher level
6 A fixed amount of an ideal gas is trapped in a container of volume V.
The pressure exerted by the gas is P and its absolute temperature is T.
a Using a sketch of PV against T, explain how you can determine the number of moles
of gas within the container.
b Sketch a graph of PV against P when the gas is kept at a constant temperature.
Explain the shape of the graph.
7 A rigid cylinder of volume 0.030 m3 holds 4.0 g of air. The molar mass of air is about 29 g.
a Calculate the pressure exerted by the air when its temperature is 34 °C.
b What is the temperature of the gas in degrees Celsius when the pressure is twice
your value from part a?
[4]
[3]
[4]
[4]
16
8 The diagram shows two insulated containers holding gas.
The containers are connected together by tubes of negligible volume.
The internal volume of each container is 2.0 × 10–2 m3.
The temperature within each container is –13 °C. The gas in container A exerts a pressure
of 180 kPa and the gas in container B exerts a pressure of 300 kPa.
a Show that the amount of gas within the two containers is about 4.4 moles.
b The valve connecting the containers is slowly opened and the gases are allowed to mix.
The temperature within the containers remains the same.
Calculate the new pressure exerted by the gas within the containers.
9 The diagram shows a cylinder containing air
at a temperature of 5.0 °C.
A force of 400 N is applied normally to the
piston of cross-sectional area 1.6 × 10–3 m2.
The volume occupied by the compressed air
is 2.4 × 10–4 m3.
The molar mass of air is about 29 g.
a Calculate the pressure exerted by the compressed air.
b Determine the number of moles of air inside the cylinder.
c Use your answer to b to determine:
i the mass of air inside the cylinder
ii the density of the air inside the cylinder.
10 The mean speed of a helium atom at a temperature of 0 °C is 1.3 km s–1. Estimate the mean
speed of helium atoms on the surface of a star where the temperature is 10 000 K.
11 The surface temperature of the Sun is about 5400 K. On its surface, particles behave like the
atoms of an ideal gas. The atmosphere of the Sun mainly consists of hydrogen nuclei.
These nuclei move in random motion.
a Explain what is meant by random motion.
b For hydrogen nuclei on the surface of the Sun:
i calculate the mean translational kinetic energy
ii estimate the mean speed.
(The mass of hydrogen nucleus is 1.7  10−27 kg.)
[3]
[3]
[2]
[3]
[1]
[2]
[6]
[1]
[2]
[3]
Extension
12 a Calculate the mean translational kinetic energy of gas atoms at 0 °C.
b Estimate the mean speed of carbon dioxide molecules at 0 °C.
The molar mass of carbon dioxide is 44 g.
c Calculate the change in the internal energy of one mole of carbon dioxide gas when its
temperature changes from 0 °C to 100 °C.
[2]
[5]
[3]
17
13 The diagram below shows three different types of arrangements of gas particles.
A gas whose particles consist of single atoms is referred to as monatomic – for example
helium (He). A gas with two atoms to a molecule is called diatomic – for example oxygen
(O2). A gas with more than two atoms to a molecule is said to be polyatomic – for example
water vapour (H2O).
A single atom can travel independently in the x, y and z directions: it is said to have three
degrees of freedom. From the equation for the mean translational kinetic energy of the atom,
1
we can generalise that a gas particle has mean energy of kT per degree of freedom.
2
Molecules can also have additional degrees of freedom due to their rotational energy.
a Use the diagram above to explain why:
5
i the mean energy of a diatomic molecule is kT
2
ii the mean energy of a polyatomic molecule is 3kT.
b Calculate the internal energy of one mole of water vapour (steam) per unit kelvin.
Total:
75
Score:
[2]
[2]
[3]
%
18
8 Electric fields
permittivity of free space ε0 = 8.85 × 10–12 F m–1
elementary charge e = 1.6 × 10–19 C
Intermediate level
1 State two possible SI units for electric field strength.
[2]
2 A +5.0 × 10–8 C point charge experiences a force of 1.5 × 10–3 N when placed in a uniform
electric field. Calculate the electric field strength.
[2]
3 Calculate the force experienced by an oil droplet with a charge of 3.2 × 10–19 C due to a
uniform electric field of strength 5.0 × 105 V m–1.
[2]
4 The diagram shows two parallel, horizontal plates separated by a vertical distance of 3.0 cm.
The potential difference between the plates is 600 V.
a Calculate the magnitude and direction of the electric field between the plates.
b Describe the electric field between the plates.
c An oil droplet of weight 6.4 × 10–15 N is held stationary between the two plates.
i State whether the charge on the droplet is positive or negative.
Explain your answer.
ii Determine the charge on the oil droplet.
5 Draw the electric field patterns for the charged conductors shown.
a
b
c
[3]
[2]
[2]
[2]
[6]
6 Calculate the electrical force between a proton and an electron separated by a distance of
5.0 × 10–11 m.
[3]
7 The electric field strength E at a distance r from a point charge Q may be written as:
Q
E=k 2
r
What is the value for k?
[2]
19
Higher level
8 The diagram shows a point charge +q placed in the electric field of a charge +Q.
The force experienced by the charge +q at point A is F. Calculate the magnitude of the
force experienced by this charge when it is placed at points B, C, D and E. In each case,
explain your answer.
9 A spherical metal dome of radius 15 cm is electrically charged. It has a positive charge of
+2.5 μC distributed uniformly on its surface.
a Calculate the electric field strength on the surface of the dome.
b Explain how your answer to a would change at a distance of 30 cm from the surface of
the dome.
10 The diagram shows two point charges.
The point X is midway between the charges.
Calculate the electric field strength at point X due to:
i the + 20 μC charge
ii the + 40 μC charge.
b Calculate the resultant electric field strength at point X.
[9]
[3]
[2]
a
[3]
[2]
[2]
11 Describe some of the similarities and differences between the electrical force due to a point
charge and the gravitational force due to a point mass.
[6]
Extension
12 The diagram shows two point charges.
Calculate the distance x of point P from
charge +Q where the net electric field
strength is zero.
[6]
13 Show that the ratio:
electrical force between two protons
gravitatio nal force between two protons
is about 1036 and is independent of the actual separation between the protons.
(Mass of a proton = 1.7 × 10–27 kg; gravitational constant G = 6.67 × 10–11 N m2 kg–2.)
[5]
Total:
64
Score:
%
20
9 Magnetic fields (1)
Intermediate level
1 Explain what is meant by electromagnetism.
[1]
2 Explain why a current-carrying conductor placed in an external magnetic field experiences
a force.
[1]
3 In Fleming’s left-hand rule, the seCond finger shows the direction of the Current.
What type of current is it?
[1]
4 A current-carrying conductor is placed in an external magnetic field. In each case below, use
Fleming’s left-hand rule to predict the direction of the force on the conductor.
a
[1]
b
[1]
c
[1]
5 The unit of magnetic flux density is the tesla. Show that:
1 T = 1 N A–1 m–1
[2]
6 Calculate the force per centimetre length of a straight wire placed at right angles to a uniform
magnetic field of magnetic flux density 0.12 T and carrying a current of 3.5 A.
[3]
21
Higher level
7 The diagram shows a rectangular metal
frame PQRS placed in a uniform
magnetic field.
The magnetic flux density is 4.5 × 10–3 T. The current in the metal frame is 2.5 A.
a Calculate the force experienced by side PQ of the frame.
[3]
b Suggest why side QR does not experience a force.
[1]
c Describe the motion of the frame immediately after the current in the frame is switched on. [2]
8 A current-carrying conductor placed at right angles to a uniform magnetic field, experiences a
force of 4.70 × 10–3 N. Determine the force on the wire when, separately:
a the current in the wire is increased by a factor of 3.0
[2]
b the magnetic flux density is halved
[2]
c the length of the wire in the magnetic field is reduced to 40% of its original length.
[2]
9 The diagram shows a currentcarrying wire frame placed
between a pair of Magnadur
magnets on a yoke.
A small pointer is connected
to a section of the wire in the
magnetic field. The position
of the pointer is noted.
A current of 8.5 A in the
wire causes the pointer to
move vertically upwards.
A small paper tape is
attached on to the pointer.
Using a pair of scissors, its length is shortened until the pointer returns back to its original
position. The paper tape is found to have a mass of 60 mg. The section of the wire between
the poles of the magnetic has a length of 5.2 cm.
a What is the direction of the magnetic field?
[1]
b Calculate the force on the wire due to the magnetic field when it carries a current of 8.5 A. [2]
c Calculate the magnetic flux density of the magnetic field between the poles of the magnet. [3]
Extension
10 The diagram shows a current-carrying conductor placed at an angle to a uniform magnetic
field.
22
Magnetic flux density is a vector. Use this idea to derive an equation for the force F acting
on the wire in terms of the magnetic flux density B, the current I, the length L of the wire
in the field and the angle θ between the magnetic field and the wire.
[3]
11 The diagram shows the rectangular loop PQRS of a simple electric motor placed in a
uniform magnetic field of flux density B.
The current in the loop is I. The lengths PQ and RS are both L and lengths QR and SP
are both x.
Show that the torque of the couple acting on the loop for a given current and magnetic flux
density is directly proportional to the area of the loop.
Total:
37
Score:
[5]
%
23
9 Magnetic fields (2)
elementary charge e = 1.6 × 10–19 C
mass of electron = 9.1 × 10–31 kg
Intermediate level
1
2
3
A current-carrying wire is placed in a uniform magnetic field.
a When does the wire experience the maximum force due to the magnetic field?
b When does the current-carrying wire experience no force due to the magnetic field?
A 4.0 cm long conductor carrying a current of 3.0 A is placed in a uniform magnetic field
of flux density 50 mT. In each of a, b and c below, determine the size of the force acting
on the conductor.
a
b
c
5
[6]
A copper wire carrying a current of 1.2 A
has 3.0 cm of its length placed in a uniform
magnetic field. The force experienced by
the wire is 3.8 × 10–3 N when the angle
between the wire and the magnetic field
is 50°.
a Calculate the magnetic field strength.
b What is the direction of the force experienced by the wire?
4
[1]
[1]
Calculate the force experienced by an electron travelling at a velocity of 4.0 × 106 m s–1
at right-angles to a magnetic field of magnetic flux density 0.18 T.
The diagram shows an electron moving at a
constant speed of 8.0 × 106 m s–1 in a plane
perpendicular to a uniform magnetic field
of magnetic flux density 4.0 mT.
a Calculate the force acting on the
electron due to the magnetic field.
[3]
b What is the centripetal acceleration
of the electron?
[2]
c Use your answer to b to determine
the radius of the circular path
described by the electron.
[2]
[3]
[1]
[3]
Higher level
6
The diagram shows the trajectory of an electron travelling into a region of uniform magnetic
field of flux density 2.0 mT. The electron enters the region of magnetic field at 90°.
24
a Draw the direction of the force experienced by the electron at points A and B.
b Explain why the electron describes part of a circular path while in the region of the
magnetic field.
c The radius of curvature of the path of the electron in the magnetic field is 5.0 cm.
Calculate the speed v of the electron.
d Explain how your answer to c would change if the electron described a circular path
of radius 2.5 cm.
7
A proton of kinetic energy 15 keV travelling at right-angles to a magnetic field describes
a circle of radius of 5.0 cm. The mass of a proton is 1.7 × 10–27 kg.
a Show that the speed of the proton is 1.7 × 106 m s–1.
b For this proton, calculate the centripetal force provided by the magnetic field.
c Determine the magnetic flux density of the magnetic field that keeps the proton moving
in its circular orbit.
d How long does it take for the proton to complete one orbit?
[1]
[1]
[5]
[2]
[3]
[3]
[3]
[2]
Extension
8
The diagram shows a velocity-selector for charged ions. Ions of a particular speed emerge
from the slit.
The parallel plates have a separation of 2.4 cm and are connected to a 5.0 kV supply.
A magnetic field is applied at right-angles to the electric field between the plates such
that the positively charged ions emerge from the slit of the velocity-selector at a speed of 6.0 × 106 m s–1.
Calculate the magnetic flux density of the magnetic field.
[6]
9
An electron describes a circular orbit in a plane perpendicular to a uniform magnetic field.
Show that the time T taken by an electron to complete one orbit in the magnetic field is independent of its speed
and its radius, and is given by:
T=
2πm
Be
25
where B is the magnetic flux density of the magnetic field, e is the charge on an electron
and m is the mass of an electron.
Total:
53
Score:
[5]
%
26
10 Electromagnetic induction
Intermediate level
1 A flat coil of N turns and cross-sectional area A is placed in a uniform magnetic field of flux
density B. The plane of the coil is normal to the magnetic field.
a Write an equation for:
i the magnetic flux  through the coil
[1]
ii the magnetic flux linkage for the coil. [1]
b The diagram shows the coil when the
magnetic field is at an angle θ to the
normal of the plane of the coil.
What is the flux linkage for the coil?
[1]
2 A square coil of N turns is placed
in a uniform magnetic field of
magnetic flux density B.
Each side of the coil has length x.
What is the magnetic flux linkage
for this coil?
3 The diagram shows a magnet placed
close to a flat circular coil.
a Explain why there is no
induced e.m.f. even though
there is magnetic flux linking
the coil.
b Explain why there is an induced
e.m.f. when the magnet is
pushed towards the coil.
[2]
[1]
[2]
4 A coil of cross-sectional area
4.0 × 10–4 m2 and 70 turns is placed
in a uniform magnetic field.
a The plane of the coil is at rightangles to the magnetic field.
Calculate the magnetic flux
density when the flux linkage
for the coil is 1.4 × 10–4 Wb.
[3]
b The coil is placed in a magnetic field of flux density 0.50 T.
The normal to the coil is at an angle of 60° to the magnetic field, as shown in the diagram.
Calculate the flux linkage for the coil.
[3]
5 A square coil is placed in a uniform
magnetic field of flux density 40 mT.
27
The plane of the coil is normal to the
magnetic field. The coil has 200 turns
and the length of each side of the coil
is 3.0 cm.
a
Calculate:
i the magnetic flux  through the coil
ii the magnetic flux linkage for the coil.
b The plane of the coil is turned through 90°. What is the change in the magnetic flux
linkage for the coil?
[2]
[2]
[2]
Higher level
6 A flat circular coil of 1200 turns and of mean
radius 8.0 mm is connected to an ammeter of
negligible resistance. The coil has a resistance
of 6.3 Ω. The plane of the coil is placed at rightangles to a magnetic field of flux density 0.15 T
from a solenoid.
The current in the solenoid is switched off.
It takes 20 ms for the magnetic field to decrease
from its maximum value to zero. Calculate:
a the average magnitude of the induced e.m.f. across the ends of the coil
b the average current measured by the ammeter.
7 The diagram shows a straight
wire of length 10 cm moved
at a constant speed of 2.0 m s–1
in a uniform magnetic field of
flux density 0.050 T.
For a period of 1 second, calculate:
a the distance travelled by the wire
b the area swept by the wire
c the change in the magnetic flux for the wire (or the magnetic flux ‘cut’ by the wire)
d the e.m.f. induced across the ends of the wire using your answer to c
e the e.m.f. induced across the ends of the wire using E = BvL.
[5]
[2]
[1]
[1]
[2]
[2]
[1]
8 A circular coil of radius 1.2 cm has 2000 turns. The coil is placed at right-angles to a magnetic
field of flux density 60 mT. Calculate the average magnitude of the induced e.m.f. across the
ends of the coil when the direction of the magnetic field is reversed in a time of 30 ms.
[5]
28
Extension
9 The diagram below shows a
step-up transformer.
The primary coil has 1150 turns
and the secondary coil has 30 turns.
The ends of the secondary coil are
connected to a lamp labelled as
‘6.0 V, 24 W’. The ends AB of the
primary coil are connected to a
1.5 V cell and a switch. The switch
is initially closed and the lamp is off.
The switch is suddenly opened and the
lamp illuminates for a short time.
a Explain why the lamp illuminates only for a short period.
b The cell and the switch are disconnected from the primary coil. The ends AB are now
connected to an alternating voltage supply. The potential difference across the lamp is
6.0 V.
i Calculate the current in the lamp.
ii What is the input voltage to the primary coil?
10 The diagram shows a square coil about to enter
a region of uniform magnetic field of magnetic
flux density 0.30 T.
[4]
[2]
[2]
The magnetic field is at right-angles to the plane
of the coil. The coil has 150 turns and each side is
2.0 cm in length. The coil moves at a constant
speed of 0.50 m s–1.
a
i Calculate the time taken for the coil to enter completely the region of magnetic field.
ii Determine the magnetic flux linkage through the coil when it is all within the region
of magnetic field.
b Explain why the induced e.m.f. is constant when the coil is entering the magnetic field.
c Use your answer to a to determine the induced e.m.f. across the ends of the coil.
d What is the induced e.m.f. across the ends of the coil when it is completely within the
magnetic field? Explain your answer.
[1]
[2]
[1]
[4]
[2]
11 A wire of length L is placed in a uniform magnetic field of flux density B.
The wire is moved at a constant velocity v at right-angles to the magnetic field.
Use Faraday’s law of electromagnetic induction to show that the induced e.m.f. E across the
ends of the wire is given by E = BvL.
Hence calculate the e.m.f. induced across the ends of a 20 cm long rod rolling along a
horizontal table at a speed of 0.30 m s–1. (The vertical component of the Earth’s magnetic
flux density is about 40 μT.)
Total:
65
Score:
[8]
%
29
11 Capacitors
Intermediate level
1 A 30 μF capacitor is connected to a 9.0 V battery.
a Calculate the charge on the capacitor.
b How many excess electrons are there on the negative plate of the capacitor?
(Elementary charge e = 1.6 × 10–19 C)
[2]
[2]
2 The p.d. across a capacitor is 3.0 V and the charge on the capacitor is 150 nC.
Determine the charge on the capacitor when the p.d. is:
a 6.0 V
b 9.0 V.
[2]
[2]
3 A 1000 μF capacitor is charged to a potential difference of 9.0 V.
a Calculate the energy stored by the capacitor.
b Determine the energy stored by the capacitor when the p.d. across it is doubled.
[2]
[2]
4 For each circuit below, determine the total capacitance of the circuit.
[14]
5 The diagram shows an electrical circuit.
a
b
c
d
Calculate the total capacitance of the two capacitors in parallel.
What is the potential difference across each capacitor?
Calculate the total charge stored by the circuit.
Calculate the total energy stored by the capacitors.
[2]
[1]
[2]
[2]
30
Higher level
6 A 10 000 μF capacitor is charged to its maximum operating voltage of 32 V.
The charged capacitor is discharged through a filament lamp. The flash of light from
the lamp lasts for 300 ms.
a Calculate the energy stored by the capacitor.
b Determine the average power dissipated in the filament lamp.
[2]
[2]
7 The diagram shows a 1000 μF capacitor charged to a p.d. of 12 V.
a Calculate the charge on the 1000 μF capacitor.
[2]
b The 1000 μF capacitor is connected across an uncharged 500 μF capacitor by closing
the switch S. The charge initially stored by the 1000 μF capacitor is now shared with
the 500 μF capacitor.
i Calculate the total capacitance of the capacitors in parallel.
ii Show that the p.d. across each capacitor is 8.0 V.
[2]
[2]
8 A charged capacitor is connected across a resistor of resistance 100 kΩ. The graph below
shows the variation of p.d. V across the capacitor with time t.
Use the graph to determine:
a the initial current in the circuit
b the time constant of the circuit
c the capacitance C of the capacitor. (Hint: use your answer to b.)
[2]
[2]
[2]
31
9 A 220 μF capacitor is charged to a potential difference of 8.0 V and then discharged through
a resistor of resistance 1.2 MΩ.
a Determine the time constant τ of the circuit.
b Calculate:
i the initial current in the circuit
ii the current in the circuit after a time equal to 2τ
iii the p.d. across the capacitor after a time of 50 s.
[2]
[2]
[2]
[3]
Extension
10 A 100 μF capacitor is discharged through a resistor of resistance 470 kΩ.
Determine the ‘half-life’ of this circuit. (The half-life of the circuit is the time taken for
the voltage across the capacitor to decrease to 50% of its initial value.)
[5]
11 The diagram below shows a charged capacitor of capacitance C. When the switch S is closed,
this capacitor is connected across the uncharged capacitor of capacitance 2C.
Calculate the percentage of energy lost as heat in the resistor and explain why the actual
resistance of the resistor is irrelevant.
[7]
Total:
70
Score:
%
32
12 Atomic structure
elementary charge e = 1.6  1019 C
speed of light in a vacuum c = 3.0  108 m s1
Planck constant h = 6.63  1034 J s
permittivity of free space = 8.85  1012 F m1
mass of neutron  mass of proton  1.7  1027 kg
mass of electron = 9.1  1031 kg
Intermediate level
1 State what may be concluded about the structure of the atom from the following observations
made in the Rutherford α-scattering experiment.
a Most of the α-particles went straight through the gold foil without much scatter.
b A very small percentage of the positively charged α-particles were scattered through
large angles by the gold foil.
2 The diagram shows the trajectory of an α-particle
as it travels past the nucleus of a gold atom.
a Copy the diagram, adding arrows to show the
directions and magnitudes of the forces
experienced by the gold nucleus and the
α-particle when the α-particle is at point A.
[2]
b State a value for the typical size (diameter)
of the nucleus.
[1]
[1]
[2]
3 Define the following terms:
a proton (atomic) number
b nucleon (mass) number
c isotopes.
[1]
[1]
[1]
4 A nuclide of carbon-14 has six protons and eight neutrons.
a What is the nucleon number for this nuclide?
b How many electrons are there in a neutral atom of carbon-14?
c Represent this nuclide in the form AZ X . The chemical symbol for carbon is C.
[1]
[1]
[1]
5 Represent each of the nuclides below in the form AZ X .
a a uranium nucleus with 143 neutrons and 92 protons (chemical symbol: U)
b an α-particle, which has 2 protons and 2 neutrons (chemical symbol: He)
c a lithium nucleus with 5 neutrons and 3 protons (chemical symbol: Li)
[2]
[2]
[2]
Higher level
6 Explain the term hadron and give one example.
[2]
7 a Using the quark model, state the constituents of a neutron.
b In beta-decay, a neutron inside the nucleus of an unstable atom decays into a proton, an
electron and an antineutrino. Show that charge is conserved in this reaction.
c The + meson is a particle with one up quark (u) and one antidown quark ( d ).
Use Table 12.4 on page 189 of Physics 2 to determine the charge Q, baryon number B
and strangeness S for this particle.
[1]
[2]
[3]
33
8 The radius of a tritium atom 31 H is about 5.0  1011 m.
The nucleus has one proton and two neutrons.
a Calculate the electrical force between an electron and a proton at a separation equal to
the radius of the atom.
b Name the two forces that exist between the neutron and proton.
c Electrons have negligible mass compared with the nucleons.
Estimate the density of the tritium atom.
9 The spacing between the atoms in a solid is typically 2.0 × 1010 m. For diffraction of either
X-rays or particles by the solid, the incident wavelength must be comparable to or less than
this spacing. For a wavelength of 2.0 × 1010 m, calculate:
a the frequency of X-rays
b the speed of electrons
c the speed of neutrons.
[3]
[2]
[3]
[2]
[2]
[2]
Extension
10 The diagram shows the typical diffraction pattern formed when high-speed electrons are
diffracted by the nuclei of a target material.
The angle θ for the ‘first diffraction minimum’ is related to the diameter d of a single
nucleus and the de Broglie wavelength λ of a high-speed electron by the equation:
1.22
sin θ =
d
The wavelength λ of a high-speed electron is related to its kinetic energy E, the Planck
constant h and the speed of light in vacuum c by the equation:
hc
λ=
E
a The angle θ is 52° for 420 MeV electrons fired into carbon.
Determine the diameter of a nucleus of carbon. (1 eV = 1.6 × 1019 J.)
b The mass of a single nucleus of carbon is 2.0 × 1026 kg.
Determine the mean density of the carbon nucleus.
c The density of matter is about 103 kg m3.
What does your value for the density of the nucleus suggest about the structure of atoms?
Total:
49
Score:
[4]
[3]
[2]
%
34
13 Nuclear physics
speed of light in a vacuum, c = 3.0 × 108 m s1
unified atomic mass unit, u = 1.66 × 1027 kg
1 eV = 1.6 × 1019 J
Intermediate level
1 a Write Einstein’s famous equation relating mass and energy.
b Determine the change in energy equivalent to a change in mass:
i of 1.0 g
ii equal to that of an electron (9.1 × 1031 kg).
[1]
[2]
[2]
2 In nuclear physics, it is common practice to quote the mass of a nuclear particle in terms of
the unified atomic mass unit, u. The unified atomic mass unit u is defined as one-twelfth of the
mass of an atom of the carbon isotope 126 C .
a
Determine the mass of each of the following particles in terms of u:
i an α-particle of mass 6.65 × 1027 kg
ii a carbon-13 atom of mass 2.16 × 1026 kg.
b Determine the mass of each of the following particles in kilograms:
i a proton of mass 1.01 u
ii a uranium-235 nucleus of mass 234.99 u.
[1]
[1]
[1]
[1]
3 State three quantities conserved in all nuclear reactions.
[3]
4 a Explain why external energy is required to ‘split’ a nucleus.
b Define the binding energy of a nucleus.
c The binding energy of the nuclide 168 O is 128 MeV. Calculate the binding energy
[1]
[1]
per nucleon.
[2]
5 For each nuclear reaction below, determine any missing figures.
4
?
a 228
90Th  2 He  ? Ra
b
c
d
e
2
1
?
1 H  1 H  ? He
2
3
4
1
1 H  1 H  2 He  ? 0 n
235
1
?
92
92 U  0 n  ? Ba  36 Kr
14
1
12
?
? N  0 n  6 C  1H
[1]
[1]
[1]

301 n
[1]
[1]
35
Higher level
6 Explain what is meant by a thermal neutron.
[1]
7 The binding energy per nucleon against nucleon number graph for some common nuclides is
shown below.
a Identify the most stable nuclide. Explain your answer.
b Use the graph to estimate the binding energy for the nucleus of
12
6
C.
c
Use the graph to estimate the energy released in the following fusion reaction.
2
2
4
1 H  1 H  2 He
d The fusion reaction shown in c is one of the many that occur in the interior of stars.
State the conditions necessary to initiate such reactions in stars.
8 Use the data given below to determine the binding energy and the binding energy per
nucleon of the nuclide 235
92 U .
[2]
[2]
[4]
[2]
[7]
mass of proton = 1.007 u
mass of neutron = 1.009 u mass of uranium-235 nucleus = 234.992 u
36
9 a Describe the process of induced nuclear fission.
b The diagram shows the fission of uranium-235 in accordance with the nuclear equation:
235
1
95
139
1
92 U  0 n  38 Sr  54 Xe  2 0 n
Copy the diagram, adding labels to identify the neutrons, the strontium nuclide and
the xenon nuclide.
ii Explain why energy is released in the reaction above.
iii Use the following data to determine the energy released in a single fission reaction
1
involving 235
92 U and 0 n .
[1]
i
mass of
235
92
U = 3.902 × 1025 kg mass of
mass of 01 n = 1.675 × 1027 kg
mass of
95
38
139
54
[1]
[2]
[5]
Sr = 1.575 × 1025 kg
Xe = 2.306 × 1025 kg
10 Explain the purpose of each of the following components of a nuclear fission reactor.
a the fuel elements
b the moderator
c the control rods
d the coolant
[1]
[1]
[2]
[1]
11 One of the neutron-induced fission reactions of uranium-235 may be represented by the
following nuclear equations.
235
1
236
92 U + 0 n  92 U
236
92
U 
146
57
La +
87
35
Br + 3 01 n
The binding energies per nucleon for these nuclides are:
236
146
87
92 U, 7.59 MeV; 57 La, 8.41 MeV; 35 Br, 8.59 MeV.
Calculate the energy released in MeV when the
236
92
U
nucleus undergoes fission.
[3]
Extension
12 In a process referred to as ‘annihilation’, a particle interacts with its antiparticle and the
entire mass of the combined particles is transformed into energy in the form of photons.
The following equation represents the interaction of a proton (p) and its antiparticle, the
antiproton ( p ).
1
1
1 p  1 p
γγ
The antiproton has the same mass as a proton – the only difference is that it has a negative
charge. Determine the wavelength  of each of the two identical photons emitted in the
reaction above. (Mass of a proton = 1.7 × 1027 kg.)
[5]
13 Does fusion or fission produce more energy per kilogram of fuel? Answer this question by
considering the fusion reaction in 7 c and the fission reaction in 9 b.
(The molar masses of hydrogen-2 and uranium-235 are 2 g and 235 g, respectively.)
[7]
Total:
68
Score:
%
37
14 Radioacivity
Intermediate level
1 a
Give the name of each of the following ionising radiations:
i 42 He
ii 01 e
iii γ
b Which radiation is the most ionising?
c What is wrong with the statement below written by a student in his notes?
Beta-particles emitted from a radioactive material are electrons that have been ejected
from their orbits around the atoms.
2 State two of the properties of γ-radiation.
In each case below, write a nuclear decay equation.
i The polonium isotope 210
84 Po emits an α-particle and changes into an isotope of
lead (Pb).
ii The strontium isotope 90
38 Sr emits a β-particle and changes into an isotope of
yttrium (Y).
b Explain why the nucleon number in your answer to a ii does not change.
[3]
[1]
[1]
[2]
3 a
[2]
[2]
[2]
4 During the transformation of the thorium isotope 232
90Th into an isotope of radon (Rn),
a total of three α-particles and two β-particles are emitted. Determine the nucleon number
and proton number of the isotope of radon.
[4]
5 The two types of beta decay are beta-plus (+) and beta-minus ().
a Name the force responsible for both types of beta decay.
b What is the beta-plus particle?
c Describe each type of decay in terms of the simple quark model.
[1]
[2]
[2]
6 a Define the half-life of a radioactive isotope.
b The half-life of a particular isotope is 20 minutes. A sample initially contains N0 nuclei
of this isotope. Determine the number of nuclei of the isotope left in the sample after:
i 20 minutes
ii 1.0 hour.
7 The activity of an α-source is 540 Bq. The kinetic energy of each α-particle is 8.6 × 1014 J.
The isotope in the source has a very long half-life.
a Calculate the number of α-particles emitted by the source in:
i 1 second
ii 1 hour.
b Determine the total energy released by the source in a time of 1 second.
c State the rate at which energy is emitted from this α-source.
[1]
[1]
[2]
[1]
[1]
[3]
[1]
38
Higher level
8 The half-life of the radon isotope 220
86 Rn is 56 s.
a Determine the decay constant in s1.
b Calculate the activity of a sample containing 6.0 × 1010 nuclei of
220
86 Rn
[3]
[3]
.
9 The activity of a radioactive source containing 8.0 × 1014 undecayed nuclei is 5.0 × 109 Bq.
a Determine the decay constant in s1.
b Calculate the half-life of the nucleus.
c How many undecayed nuclei will be left after 40 hours?
10 a Define the decay constant of a nucleus.
b The thorium isotope 227
90 Th has a half-life of 18 days.
[1]
A particular radioactive source contains 4.0 × 1012 nuclei of the isotope
i Determine the decay constant for the thorium isotope
ii What is the initial activity of the source?
iii Calculate the activity of the source after 36 days.
[3]
[3]
[3]
227
90 Th
227
90 Th
.
1
in s .
[3]
[3]
[2]
11 A sample of rock is known to contain 1.0 μg of the radioactive radium isotope 226
88 Ra .
The half-life of this particular isotope is 1600 years. The molar mass of radium-226 is 226 g.
a Determine the number of nuclei of the isotope 226
88 Ra in the rock sample.
b Calculate the activity from decay of the radium-226 in the sample.
[2]
[3]
Extension
12 Some astronomers believe that our Solar System was formed 5.0 × 109 years ago.
Assuming that all uranium-238 nuclei were formed before this time, what fraction of the
original uranium-238 nuclei remain in the Solar System today? The isotope of uranium
238
9
92 U has a half-life of 4.5 × 10 y.
[4]
13 A student records the initial count rate from a radioactive sample as 340 counts per second.
The count rate after 26 minutes is 210 counts per second. Calculate the half-life of each
nuclide within the radioactive sample.
[7]
14 Compare and contrast the decay of radioactive nuclei and the decay of charge on a capacitor
in a C–R circuit.
[5]
Total:
77
Score:
%
39
15 X-rays
speed of light in a vacuum c = 3.0  108 m s1
Planck constant h = 6.63  1034 J s
mass of electron = 9.11  1031 kg
1 eV = 1.6  1019 J
Intermediate level
1 State the nature of X-ray radiation.
[2]
2 The energy of an X-ray photon is 50 keV.
a Calculate the energy of the photon in joules.
b Calculate the wavelength of the X-rays.
[2]
[2]
3 One of the interaction mechanisms between X-rays and matter is the photoelectric effect.
Name the two other interaction mechanisms.
[2]
4 State one main difference between the images produced by a normal X-ray machine and by
a CAT scan.
[1]
5 Briefly explain what is meant by a non-invasive technique.
[1]
Higher level
6 Briefly describe the production of X-rays and explain why an X-ray spectrum may consist
of a continuous spectrum and a line spectrum.
[7]
7 The intensity of a collimated X-ray beam is 250 W m2.
a Define intensity.
b The diameter of the X-ray beam is 4.0 mm. Calculate the power transmitted by the beam.
[1]
[2]
8 Describe what is meant by a contrast medium and state why it is used in X-ray scans.
[2]
9 The potential difference between the cathode and the anode of an X-ray tube is 80 kV.
Calculate the minimum wavelength of the X-rays emitted from this tube.
[3]
10 The photoelectric effect is one of the attenuation mechanisms by which X-ray photons
interact with the atoms in the body. Describe some of the characteristics of this mechanism.
[3]
11 A collimated X-ray beam is incident on a metal block. The incident intensity of the beam is I0.
a Draw a sketch graph to show the variation with thickness x of the intensity I of the beam. [3]
b Write down an expression for the intensity I in terms of I0 and x.
Explain any other symbol you use.
[2]
c The linear absorption coefficient of a beam of 80 keV X-rays is 0.693 mm1 in copper.
Calculate the thickness of copper necessary to reduce the intensity of the beam to 0.10 I0. [3]
12 a Describe the use of a CAT scanner.
b Compare the image formed in X-ray diagnosis with that produced by a CAT scanner.
[5]
[3]
40
Extension
13 X-rays are attenuated by soft tissues. The graph below shows how lg(attenuation coefficient)
varies with lg(photon energy) for three attenuation mechanisms.
a Match the labelled graphs A, B and C with the correct attenuation mechanism.
b The gradient of the straight line graph A is –3.
Deduce the relation between the attenuation coefficient  and photon energy E.
c Explain the significance of the minimum X-ray photon energy of 1.02 MeV for graph C.
d Describe the variation of the combined attenuation of X-rays with photon energy.
Total:
53
Score:
[1]
[2]
[3]
[3]
%
41
16 Diagnostic methods in medicine
speed of light in a vacuum c = 3.0  108 m s1
mass of electron or positron = 9.11  1031 kg
1 eV = 1.6  1019 J
Intermediate level
1
a Name a medical tracer other than technetium-99m.
b State three uses of technetium-99m as a tracer in the body.
c Suggest why technetium-99m has a limited ‘shelf life’.
[1]
[3]
[1]
2
Name the four main components of a gamma camera.
[4]
3
State one similarity and one difference between the techniques of CAT and PET.
[2]
4
Name the five main components of an MRI scanner.
[5]
5
Protons have a precession frequency of 40 MHz in a strong uniform magnetic field.
a Describe what is meant by precession.
b State the frequency of the radio frequency (RF) radiation that will cause the protons to
resonate.
c Use your answer to b to determine the wavelength of the RF radiation.
[1]
[1]
[2]
Higher level
6
7
8
The radiopharmaceutical used in PET is often fluorine-18. This decays by emitting positrons.
a Explain the stages that lead from the emission of positrons to the formation of an image
in a PET scanner.
b Calculate the energy in electronvolts (eV) of each gamma-ray photon detected by the
PET scanner.
a Outline the principles of magnetic resonance.
b Outline, with the aid of a sketch diagram, the use of MRI (magnetic resonance imaging)
to obtain diagnostic information about internal body structures.
Describe some of the advantages and disadvantages of MRI.
[5]
[4]
[6]
[10]
[6]
Extension
9
X-Rays, ultrasound and MRI are all used in medical diagnosis.
State one situation in which each of these techniques is preferred and give reasons, one in
each case, for the choice.
Total:
57
Score:
[6]
%
42
17 Using ultrasound in medicine
Intermediate level
1
State what is meant by ultrasound.
[2]
2
The speed of ultrasound in soft tissue is 1.5 km s1.
a Calculate the wavelength of ultrasound of frequency 1.8 MHz.
b Use your answer to part a to explain why high-frequency ultrasound is suitable for
medical scans.
[2]
3
Define acoustic impedance.
[1]
4
The table below shows useful data for biological materials.
Density/kg m3
Material
Speed of
ultrasound/m s1
[1]
Acoustic impedance
Z/106 kg m2 s1
soft tissue
1060
1540
1.63
muscle
1075
1590
1.71
bone
?
4000
6.40
blood
1060
1570
1.66
a Calculate the density of bone.
b Calculate the percentage of intensity of ultrasound reflected at the blood–soft tissue
boundary. (Assume the waves are incident at right angles to the boundary.)
c Explain why it would be difficult to distinguish between blood and soft tissue in an
ultrasound scan.
[2]
[3]
[2]
Higher level
5
Outline how ultrasound may be used in medical diagnosis.
[5]
6
Explain why, in medical diagnosis using ultrasound, a coupling medium is necessary
between the ultrasound probe and the skin.
[6]
7
a
When an ultrasound pulse reflects from the front and back edges of a bone, it produces
two peaks on an A-scan. The time interval between these two peaks is 13 s. The speed
of the ultrasound in bone is 4000 m s1. Calculate the thickness of the bone.
b Describe how a B-scan differs from an A-scan.
[3]
[2]
Extension
8
In hospital radiography departments, the Doppler effect is successfully used to determine the
rate of blood flow and heartbeat of patients.
a Suggest how the Doppler effect can also be used to determine the rate of heartbeat.
b A transducer emits ultrasound of frequency f of 6.4 MHz. The change in the frequency
f of the ultrasound due to the movement of blood is 1.2 kHz. The speed c of ultrasound
in blood is 1500 m s1. The angle  between the transducer and the blood vessel is 60°.
Use the following equation to determine the speed v of the blood.
2 fv cos
f 
[2]
[2]
c
Total:
33
Score:
%
43
18 The nature of the universe
gravitational constant G = 6.67 ×1011 N m2 kg2
speed of light in a vacuum c = 3.0 ×108 m s1
Intermediate level
1 State the principal content of the universe.
[3]
2 a Define the astronomical unit (AU) and state to two significant figures its value in metres.
b The distances between stars are not measured in astronomical units.
State a convenient unit used to measure the vast distances between stars.
[2]
3 a Define the light-year (ly).
b Determine to two significant figures the distance of one light-year in metres.
c Sirius is one of the brightest stars in the night sky. Sirius is 8.7 light-years from our Sun.
Calculate this distance in metres.
[1]
[2]
4 a
[1]
State to two significant figures a value for the parsec (pc) in metres.
1 parsec
b Determine the ratio:
1 AU
[1]
[2]
[2]
5 Our Sun is about 30 000 light-years from the centre of our galaxy, the Milky Way.
Calculate this distance in parsecs.
[2]
6 a Name the type of nuclear reaction responsible for the generation of energy in stars.
b Calculate the energy released by the loss of 1 milligram of matter.
[1]
[3]
7 Describe how a dust cloud containing hydrogen and helium evolves into a star.
[5]
8 a State Hubble’s law.
b
[1]
c
Use the graph above to determine a value for the Hubble constant H0 in km s1 Mpc1.
[3]
Use your answer to part b to estimate the distance in Mpc of a galaxy moving at a velocity
of 9000 km s1 relative to our solar system.
[2]
9 Explain Olbers’ paradox and state two assumptions it makes about the universe.
10 State the three important aspects of the cosmological principle as applied to the universe.
[4]
[3]
44
Higher level
11 The energy in the interior of the Sun is produced from hydrogen burning. This process may
be summarised by the nuclear equation below, which shows the fusion of hydrogen nuclei:
411 H  42 He + 210 e + 2
a Explain why extremely high temperatures (108 K) are required for fusion reactions
to occur within the interior of stars.
b Identify the particles 42 He , 10 e and .
c In the reaction shown above, there is an overall decrease in mass of 4.4 × 1027 kg.
Calculate the energy released in the reaction.
[2]
[3]
[3]
12 Describe the fate of a star:
a such as our Sun
b much more massive than our Sun.
[1]
[1]
13 The typical density of a neutron star is 3.0 × 1017 kg m3. Calculate the radius of a neutron
star with a mass equal to five solar masses. (Solar mass = 2.0 × 1030 kg.)
[4]
14 The distance d of a star in parsecs and its parallax p in arc seconds are related by the equation
1
d
p
a The star Arcturus has a parallax of 0.09 arc seconds. How far is it from the Earth?
b The parallax technique can be used successfully to determine the distances of stars to a
maximum distance of 100 pc. Calculate the parallax, in arc seconds, for this maximum
distance.
15 In the laboratory, a particular spectral line from hydrogen atoms has a wavelength of 2.1 cm.
Calculate the change in the wavelength of the same spectral line from hydrogen atoms of
a galaxy receding from the Earth at a speed of 8000 km s1
16 A particular galaxy at 80 Mpc is found to have a recession speed of 6000 km s1.
a Use the information given to calculate a possible value for the Hubble constant in:
i km s1 Mpc1
ii s1.
b Use your answer to part a ii to show that the age of the universe is about
13 000 million years.
c Hence determine the furthest observable distance in metres for the universe.
[1]
[1]
[3]
[2]
[2]
[3]
[3]
Extension
17 A black hole is an object that results from the death of a star with a mass greater than 10 solar
masses. The maximum radius R of a black hole is given by:
2GM
R=
c2
where G is the gravitational constant, M is the mass of the black hole and c is the speed of
light in a vacuum.
a Calculate the density of a black hole with a mass equal to 20 solar masses.
(Solar mass = 2.0 × 1030 kg)
b Use a science databook or the internet to find the diameter of the neutron and its mass.
Determine the density of a neutron. How does this density compare with your answer
to part a?
Total:
75
Score:
[4]
[4]
%
45
19 The evolution of the universe
speed of light in a vacuum c = 3.0  108 m s1
gravitational constant G = 6.67  1011 N m2 kg2
Intermediate level
1 Explain what is meant by the 3 K microwave background radiation.
[3]
2 State what can be deduced from the redshift of light from distant galaxies.
[1]
3 Explain the link between the background microwave radiation and the Big Bang model
of the universe.
[5]
4 State some of the observational evidence for the Big Bang model of the universe.
[4]
5 Suggest why it is difficult to predict the state of the universe before 1043 s.
[1]
6 Describe qualitatively the evolution of the universe after the Big Bang to the present.
[7]
Higher level
7 a Suggest why it is difficult to determine the mean density of the universe.
b With the aid of a sketch graph, describe the fate of the universe if its mean density ρ
is greater than the critical density ρ0.
[1]
8 a Write an equation for the critical density ρ0 of the universe.
b A possible value of the Hubble constant is 2.42 × 1018 s1. Use this value to determine
the critical density of the universe.
c Use your answer to b to calculate the average number of protons in a volume of 1 m3
for a flat universe. (The mass of a proton is 1.7 × 1027 kg.)
[1]
[5]
[2]
[2]
Extension
9 Most cosmologists believe that the universe originated from a Big Bang. The table below
shows how the temperature T of the universe has changed with time t since the Big Bang.
Time t after the Big Bang/s
Temperature T of the universe/K
1012
1015
106
1014
103
1012
102
107
3 × 1013
103
4 × 1017
2.7
By plotting a graph of lg t against lg T, show that the temperature T and the time t are related
by the equation:
Tnt = constant
where n is an integer. Use your graph to determine the value for n.
[7]
46
1 Worksheet
10 For a hot object at a temperature T in kelvins, the maximum wavelength max in metres
emitted by the object is given by the equation below (known as Wein’s law):
 max T  0.00289
a Copy and complete the table below, assuming this equation can be applied to the universe. [2]
Time from Big Bang
b
max/m
T/K
106 s
1014
103 s
1012
100 s
107
3  105 y
104
106 y
103
present
2.7
Principal radiation
gamma rays
Use your table in part a to suggest a time after the Big Bang when the universe would
have been saturated by visible light.
Total:
42
Score:
[1]
%
47