1 Kinematics
Intermediate level
1 Explain what is meant by:
a a scalar quantity
b a vector quantity.
[1]
[1]
2 Name any three scalar quantities.
[3]
3 a Define the velocity of an object.
b Use your answer to a to explain why velocity is a vector quantity.
[1]
[2]
4 Cannons are being fired in a mock battle scene. The spectators are at a safe distance of 600 m
from the cannons. Calculate how long it would take for the sound from the cannons to reach
the spectators. (Speed of sound in air = 340 m s−1.)
[2]
5 A small insect travels a distance of 24 cm in a time of 4.0 minutes. Calculate the average speed
of the insect in m s−1.
[2]
6 The displacement against time graph for an object is shown below.
a What does the gradient of a displacement against time graph represent?
b Describe the journey of the object.
c Calculate the velocity of the object at 2.0 s.
[1]
[2]
[2]
Higher level
7 A cyclist travels a distance of 3.2 km in 15 minutes. She rests for 30 minutes. She then covers
a further distance of 6.2 km in a time of 40 minutes.
Calculate the average speed of the cyclist in m s−1:
a for the first 15 minutes of the journey
[2]
b for the total journey.
[2]
8 The diagram shows the displacement against time
graph for an object.
Calculate the velocity of the object at times:
a 4.0 s
b 8.0 s.
[2]
[2]
1
9 The diagram below shows a conker moving in a horizontal circle of radius 70 cm.
The conker takes a time of 0.62 s for each revolution.
a Calculate the speed of the conker. (Hint: In a time of 0.62 s, the conker travels a distance
equal to the circumference of the circle.)
b The conker starts at point A. What is the magnitude of the displacement of the conker
from A after a time of:
i 0.31 s
ii 0.62 s?
[2]
[1]
[1]
Extension
10 The table below shows the time taken t and the displacement s of a trolley rolling down a ramp.
Time t/s
0
0.1
0.2
0.3
0.4
0.5
0.6
Displacement s/10−2 m
0
0.8
3.0
6.8
12.0
18.9
27.0
a Plot a graph of displacement against time. (Make sure that you sketch a smooth curve.)
b Describe the motion of the trolley. Explain your answer.
c By drawing tangents to the curve at times 0.2 s and 0.5 s, determine the velocities of the
trolley at these times (see page 8 of Physics 1).
d The acceleration a of the trolley is given by:
a
[2]
[2]
[2]
change in velocit y
time taken
Use the equation above and your answers to c to determine the acceleration a of the trolley. [2]
Total:
37
Score:
%
2
2 Accelerated motion
Intermediate level
1 Define acceleration and state whether it is a scalar or a vector.
[2]
2 A footballer kicks a ball from rest. The foot is in contact with the ball for 0.30 s and the final
velocity of the ball is 15 m s−1. What is the average acceleration of the ball?
[3]
3 The diagram shows the velocity against time graph for an object.
a Describe the motion of the object.
b Calculate the acceleration of the object.
c Use the graph to determine the distance travelled by the object in 8.0 s.
[1]
[3]
[3]
4 A car slows down from a velocity of 22 m s−1 to 5.0 m s−1 in a period of 6.0 s.
For this car, calculate:
a its deceleration
b its average velocity
c the distance travelled in 6.0 s.
[3]
[1]
[2]
Higher level
5 A painter accidentally drops a can of paint from a bridge over a river. The can is in free fall for
a time of 2.3 s before it hits the water below. The acceleration of free fall is 9.81 m s−2.
a Calculate the velocity of the can just before it hits the water.
[3]
b What is the height of the bridge?
[3]
6 A cyclist is travelling at a constant velocity of 4.0 m s−1. She suddenly accelerates at 0.45 m s−2
for a distance of 9.0 m. Calculate her final velocity.
[3]
7 A racing car travelling at a velocity of 45 m s−1 hits a safety barrier. The car comes to a halt
after travelling a distance of 20 m. Calculate the average deceleration of the car.
[3]
Extension
8 An object has a uniform acceleration a. After a time t its final velocity is v.
a Sketch a graph of velocity against time for this object.
b Hence show that the displacement of the object in this time is given by:
1
s  vt  at 2
2
9 A metal ball is dropped from a height of 6.0 m onto soft ground. The ball hits the ground and
penetrates a distance of 8.5 cm. Calculate the deceleration of the ball as it enters the ground.
You may assume that the ball decelerates uniformly. (Acceleration of free fall = 9.81 m s −2.)
[2]
[4]
[5]
3
10 The diagram shows the variation with time t of the velocity v of a car travelling along a straight
road.
a Calculate the distance travelled by the car between 4.0 s and 8.0 s.
b Calculate the acceleration of the car at 12.5 s.
c Sketch a graph of acceleration against time for the car.
Total:
48
[2]
[3]
[2]
Score:
%
4
3 Dynamics
Intermediate level
acceleration of free fall g = 9.81 m s−2
1
In the topic of dynamics, the equation F = ma is very important.
Define all the terms in this equation. [3]
2
A metal sphere is falling at a steady speed in a tube containing oil. Describe all the
forces
acting on the sphere. What is the net force on the sphere? [2]
3
Define the newton (N).
[1]
4
A 120 g apple falls off a tree. Calculate the weight of the apple.
[2]
5
The diagram shows a parachutist of mass 82 kg falling towards the Earth. In each case,
determine the net force and the acceleration of the parachutist.
a
b
c
[2]
[1]
[2]
6
The gravitational field strength on the surface of Venus is 8.77 N kg−1.
a Calculate the weight of a 5.0 kg rock on the surface of this planet.
b What is the weight of a similar rock on the Earth’s surface?
[2]
[1]
Higher level
7 The diagram shows the horizontal forces acting on a motorbike and its rider travelling along a
level road. The total mass of the rider and the motorbike is 160 kg. Determine the acceleration
of the motorbike.
[3]
5
8
A car engine provides a constant forward force. When starting from rest, the
acceleration of the
car when unloaded is a. The mass of the car increases by 50% when fully loaded. Determine
the acceleration of this fully laden car in terms of the acceleration a when it starts from rest.
[3]
Extension
9 The diagram shows the horizontal forces acting on a 920 kg car.
The total forward force acting on the car is 400 N. The drag on the car depends on its speed v
and is given by the expression:
drag = 0.3v2
At a particular instant the car is travelling at a speed of 20 m s−1. Calculate:
i the net force on the car
ii the acceleration of the car.
b Explain why you cannot use
v = u + at
to determine the velocity of the car after a time t.
a
[2]
[2]
[1]
10 The diagram shows an 80 kg person in a lift.
The normal contact force acting on the person from the base of the lift is R. Determine the
magnitude of R when the lift:
a is travelling upwards at a constant velocity of 2.0 m s−1
b is accelerated upwards at 2.3 m s−2.
[2]
[3]
11
Use the internet to investigate the motion of objects travelling through fluids (liquids
and gases). To do this, use a search engine (e.g. ‘Google’) and insert a phrase such as ‘falling
objects in air applets’ or ‘skydiver applets’. An applet is an animation or a simulation of a
physical system.
Total:
32
Score:
%
6
4 Working with vectors
acceleration of free fall g = 9.81 m s−2
Intermediate level
1 A small aeroplane travels 30 km due north and then 40 km due east.
a Draw a vector triangle for the final displacement.
b Determine the magnitude of the final displacement.
[2]
[2]
2 Calculate the magnitude of the resultant force in each case below.
a
b
c
[2]
[2]
[3]
3 The diagram shows a swimmer attempting to swim
across a river.
The swimmer swims at a velocity of 2.5 m s−1
normal to the riverbank and the velocity of the
river water is 3.0 m s−1 parallel to the riverbank.
Calculate:
a the magnitude of the actual velocity
of the swimmer
[3]
b the direction of the final velocity relative to
the riverbank.
[2]
4 In each case below, resolve the vector into two perpendicular components in the x and y directions.
a
b
[2]
c
[2]
[2]
Higher level
5 A child of mass 35 kg on a swing is pulled to one side.
The diagram shows the forces acting on the seat of the
swing when it is in equilibrium.
a What is the net force on the seat?
b Draw a triangle of forces. Hence determine:
i the tension T in the rope
ii the angle  made by the rope with the vertical.
[1]
[4]
[2]
7
6 A gardener pulls a 50 kg roller along level ground, as
shown in the diagram.
The roller moves at a steady speed along the level
ground when the handle makes an angle of 30° to the
horizontal ground and the gardener pulls with a force of
300 N along the handle.
a Calculate the horizontal component of the force 300 N.
b What is the net force in the horizontal direction? Hence determine the magnitude of the
resistive force acting on the roller.
c Determine the vertical contact force acting on the roller due to the ground.
[2]
[2]
[3]
7 A marble is flicked off the edge of a platform. The marble initially has a velocity of 2.5 m s−1
horizontally. It hits the ground after travelling a vertical distance of 2.0 m. You may assume
that air resistance has a negligible effect on the motion of the marble.
a How long does it take for the marble to travel from the edge of the platform to the ground? [2]
b Determine the range of the marble – the horizontal distance travelled by the marble before
it hits the ground.
[2]
8 A stone is thrown horizontally at a velocity of 15 m s−1 from a 120 m tall tower. You may
assume that air resistance has a negligible effect on the motion of the stone. Calculate:
a how long it remains in flight
b the horizontal distance travelled
c the magnitude of its impact velocity.
[2]
[2]
[4]
Extension
9 The diagram shows a stunt person of mass 82 kg
holding on to a rope. The person and the rope are in
equilibrium.
The rope on either side of the person makes an angle
of 5.0° to the horizontal.
a
Determine the tension T in the rope.
b
What would be the consequence of making
the angle between the rope and the horizontal
equal to zero?
[3]
[2]
10 The trajectory of a water-jet from a garden hose is as shown in the diagram.
You may assume that air resistance has a negligible effect on the motion of the water-jet. Use
the information provided above to determine the speed V of the water emerging from the pipe
and the range R.
Total:
59
Score:
[6]
%
8
5 Forces,momemts and pressure
acceleration of free fall g = 9.81 m s−2
Intermediate level
1
Define the moment of a force.
[1]
2
State two conditions that must be met for the equilibrium of an extended object.
[2]
3
The diagram shows the downward forces applied on a plastic ruler.
Deduce whether or not the ruler is in equilibrium.
4
[3]
A person of weight 820 N stands on one leg. The area of the foot in contact with the floor is
1.4 × 10−2 m2.
a Calculate the pressure exerted by the foot on the ground.
b Explain what would happen to the pressure exerted on the floor if the person stands on
tiptoe on one leg.
[2]
5
Define the torque of a couple, and give one example of a couple.
[2]
6
The diagram shows a uniform beam of
length 1.5 m and weight 60 N resting
horizontally on two supports.
a By taking moments about the support A, determine the force RB at the support B.
b Use your answer to a to calculate the force RA at support A.
[1]
[3]
[1]
Higher level
7
A ladder of mass 32 kg rests at an angle against a
smooth wall as shown in the diagram.
The centre of gravity of the ladder is at its mid-point.
a Determine the force R exerted by the wall on
the ladder by taking moments about the base
of the ladder.
b Explain why the force at the base of the ladder
was not included when doing the calculation in a.
[3]
[1]
9
8 A 62 kg person lies flat on a uniform plank of mass 15 kg. The plank, with the person lying on it,
is placed on a brick and some bathroom scales, as shown in the diagram below.
The person’s toe-to-head distance is 1.56 m. The length of the plank is also 1.56 m.
a Sketch the diagram above. On your sketch, show all the forces acting on the plank.
b The reading on the bathroom scales is 30 kg. Use this information to determine how far
the centre of gravity of the person is from the toes.
[2]
[4]
9 A flagpole of mass 25 kg is held in a
horizontal position by a cable as shown
in the diagram.
The centre of gravity of the flagpole is at
a distance of 1.5 m from the fixed end.
Determine:
a the tension T in the cable
b the vertical component of the force at
the fixed end of the pole.
[4]
[2]
Extension
10 The diagram shows a wheel of mass 20 kg
and radius 80 cm pulled by a horizontal
force F against a step of height 20 cm.
Determine the magnitude of the initial
force F so that the wheel just turns over
the step.
[4]
11 A metal rod of length 90 cm has a disc of
radius 24 cm fixed rigidly at its centre, as
shown in the diagram. The assembly is
pivoted at its centre.
Two forces, each of magnitude 30 N, are
applied normal to the rod at each end so
as to produce a turning effect on the rod.
A rope is attached to the edge of the disc to
prevent rotation. Calculate the minimum
tension T in the rope.
[4]
Total:
39
Score:
%
10
6 Forces,vehicles and safety
Intermediate level
1
2
3
Explain what is meant by the stopping distance of a car.
[1]
What are the factors that increase the thinking distance when stopping a car?
[3]
Explain how wearing seat belts in a car reduces the risks of injury in a car accident.
[2]
4
Describe how GPS is used to locate the position of a car on the Earth’s surface. [4]
5
At a particular instant, a GPS satellite is 20 000 km above a car. Calculate the time
taken for the radio signal to travel between the satellite and the car. The speed of radio waves
is 3.0  108 m s−1.
[2]
Higher level
6
A car is travelling at a constant velocity of 20 m s−1. The driver of the car sees a
pedestrian unexpectedly step onto the road. The driver applies the brakes and stops the car.
The diagram shows how the velocity v of the car changes with time t from the instant the
driver sees the pedestrian step onto the road.
a Explain why the velocity of the car remains constant for 1.0 s.
b For this car, calculate:
i the thinking distance
ii the braking distance
iii the stopping distance.
c Explain how your answer to b ii would change if the road surface were icy.
[1]
[1]
[2]
[1]
[1]
7
A car is travelling at a constant velocity of 15 m s−1 on a level road. The driver sees a
child stepping onto the road, 50 m ahead. The driver takes 0.50 s to react before applying the
brakes. The brakes decelerate the car at 6.0 m s−2. Calculate how far the car stops from where
the child stepped onto the road.
[5]
8 a
The crumple zone of a car is an important safety feature in modern cars. Explain how the
crumple zone reduces the risks of injury in a car accident.
[1]
b For a particular car of mass 850 kg the front crumples in a distance of 90 cm when the car,
initially travelling at 18 m s−1, crashes into a rigid wall. Calculate:
i the average ‘impact’ force exerted on the car during the crash
[3]
−2
ii the average deceleration of the car in terms of g. (g = 9.81 m s .)
[2]
11
Extension
9
For a particular car, the braking force is 70% of the weight of the car.
a
Show that the braking distance of the car (in metres), initially travelling at a speed v, is
given by:
braking distance  0.073v 2
b Hence determine the braking distance for this car when it brakes from a speed of 70 miles
per hour.
(Acceleration of free fall g = 9.81 m s−2; 1 mile = 1.6 km.)
10
[3]
[2]
Use the internet to investigate how safety features are employed in modern cars.
Total:
34
Score:
%
12
7 Work, energy and power (1)
acceleration of free fall g = 9.81 m s−2
Intermediate level
1
Define work done by a force. [1]
2
A force of 80 N moves an object through a distance of 7.0 m in the direction of the
force. Calculate the energy transferred by the force. [2]
3
Calculate the work done by a person of mass 72 kg in climbing a ladder 5.0 m high.
[2]
4
A car of mass 900 kg is travelling at a speed of 18 m s−1. Calculate its kinetic energy
when travelling at this speed. [2]
5
Which of the following has greater kinetic energy?
•
•
A 10 g meteor hurtling through the Earth’s atmosphere at 5.0 km s−1.
A 65 kg jogger running at 5.0 m s−1.
[3]
6
A water pump lifts 9.0 kg of water through a vertical height of 3.5 m in 1.0 minute.
Calculate:
a the gain in gravitational potential energy of the water
b the power of the pump.
[2]
[2]
Higher level
7
A ball of mass 800 g is dropped from a height of 5.0 m and rebounds to a height of 3.8
m.
The air resistance is negligible. Calculate:
a the kinetic energy of the ball just before impact
b the initial rebound speed of the ball
c the energy transferred to the ground during the impact.
[2]
[3]
[1]
8
The diagram shows a child on a swing. The mass of the child is 35 kg. The child is
raised to
point A and then released. She swings downwards through point B.
a Calculate the change in gravitational potential energy of the child between A and B.
b Assuming that air resistance is negligible, calculate the speed of the child as she passes
through the equilibrium position B.
c The rope stays taut throughout. Explain why the work done by the tension in the rope is
zero.
[2]
[2]
[1]
13
Extension
9
A bullet of mass 30 g and travelling at a speed of 200 m s−1 embeds itself in a wooden
block. The bullet penetrates a distance of 12 cm into the wood. Using the concepts of work
done by a force and kinetic energy, determine the average resistive force acting on the bullet.
[3]
10
The diagram shows a 50 kg crate being dragged by a cable up a ramp that makes an
angle of
24° with the horizontal.
The crate moves up the ramp at a constant speed and travels a total distance of 20 m up the
ramp. Determine the magnitude of the friction between the crate and the surface of the ramp.
Total:
34
Score:
[6]
%
14
7 Work, energy and power (2)
acceleration of free fall g = 9.81 m s−2
Intermediate level
1
2
State the principle of conservation of energy.
[1]
In each case below, discuss the energy changes taking place.
a An apple falling towards the ground.
b A car decelerates when the brakes are applied.
c A space probe fall towards the surface of a planet.
[1]
[1]
[1]
3
A 120 kg crate is dragged along the horizontal
ground by a 200 N force acting at an angle of
30° to the horizontal. The crate moves along
the surface with a constant velocity of 0.5 m s–1.
The 200 N force is applied for a time of 16 s.
a
Calculate the work done on the crate by:
i the 200 N force
ii the weight of the crate
iii the normal contact force R.
b Calculate the rate of work done against the frictional force FR.
4
[3]
[1]
[1]
[3]
Which of the following has greater kinetic energy?
•
•
A 20-tonne truck travelling at a speed of 30 m s–1.
A 1.2 g dust particle travelling at 150 km s–1 through space.
[3]
5
A 950 kg sack of cement is lifted to the top of a building 50 m high by an electric
motor.
a Calculate the increase in the gravitational potential energy of the sack of cement.
b The output power of the motor is 4.0 kW. Calculate how long it took to raise the sack to
the top of the building.
c The electrical power transferred by the motor is 6.9 kW. In raising the sack to the top of
the building, how much energy is wasted in the motor as heat?
6
[2]
[2]
[2]
A 200 g toy car is released from point X on a frictionless track.
The car travels downhill from X to Y. Calculate:
a the loss of gravitational potential energy between X and Y
b the speed of the toy car at point Y.
[2]
[3]
15
Higher level
7
The diagram shows two toy cars A and B at the top of frictionless tracks. The cars
have
different masses but they both drop through the same vertical height.
Which of the two cars will have a greater speed at the bottom of their track?
Explain your answer.
[4]
8
The speed of a dart of mass 120 g is reduced from 180 m s−1 to 100 m s−1 when it
passes
through a book of thickness 3.0 cm. Calculate:
a the loss of kinetic energy of the dart
b the average frictional force exerted by the book on the dart.
[3]
[3]
9
A stunt person slides down a cable that is attached between a tall building and the
ground.
The stunt person has a mass of 85 kg. The speed of the person when reaching the ground
is 20 m s−1. Calculate:
a
b
c
d
the change in gravitational potential energy of the person
the final kinetic energy of the person
the work done against friction
the average friction acting on the person.
[2]
[2]
[1]
[2]
Extension
10
A constant force is applied to an object that is initially at rest. Show that the work
done on the object, which is the same as its kinetic energy, is given by:
1 2
mv
2
16
where m is the mass of the object and v is its speed.
11
[4]
The diagram shows an object of mass m falling towards the surface of the Earth.
Assuming that there is negligible air resistance and using the principle of conservation of
energy, show that:
v2 = u2 + 2gh
where u is the initial speed of the object and v is the speed of the object after falling through a
vertical height h.
Total:
50
Score:
[3]
%
17
8 Deforming solids
acceleration of free fall g = 9.81 m s−2
Intermediate level
1
Springs and wires obey Hooke’s law. State Hooke’s law. [1]
2
A spring has a natural length of 2.5 cm. A force of 4.0 N extends the spring to a length
of 6.2 cm.
a What is the extension of the spring?
b Determine the force (spring) constant k for the spring in N m−1.
c Calculate the extension of the spring when a tensile force of 6.0 N is applied. You may
assume that the spring has not exceeded its elastic limit.
[1]
[3]
[2]
3
The diagram shows the stress against strain graphs for two wires made from different
materials.
The wires have the same length and cross-sectional area. Explain which of the materials is:
a brittle
b stiffer
c stronger.
4
[1]
[1]
[1]
A graph of force F against extension x is shown for a spring.
a Use the graph to determine the force (spring) constant k of the spring.
b Calculate the energy stored (elastic potential energy) in the spring when its extension is
5.0 cm.
[2]
[3]
18
Higher level
5
A length of cable of diameter 1.2 mm is under a tension of 150 N. Calculate the stress
in the
cable. [3]
6
A metal wire of diameter 0.68 mm and natural length 1.5 m is fixed firmly to the
ceiling at one end. When a 6.8 kg mass is hung from the free end, the wire extends by
2.8 mm. Calculate:
a the stress in the wire
b the Young modulus of the material of the wire.
[3]
[4]
7
The diagram shows two springs X and Y connected
in series and supporting a weight of 8.0 N. The force
constants of the springs are shown on the diagram.
a Calculate the extension of each spring.
b Determine the force (spring) constant for the
combination.
c According to a student, the force constant for the
springs in series is the sum of the force constants
of the individual springs. Is the student correct?
[2]
[2]
[1]
8
A 180 g trolley is placed on a frictionless air track.
One end of the trolley is attached to a spring of force
constant 50 N m−1. The trolley is pushed against a
fixed support so that the compression of the spring
is 8.0 cm. The trolley is then released.
a
What is the initial acceleration of the trolley
when it is released?
b What is the initial energy stored in the spring?
c Calculate the final speed of the trolley along the
air track. You may assume that there is 100%
transfer of energy from the spring to the trolley.
[3]
[3]
[2]
Extension
9
The force against extension graph for a length of metal wire is shown below.
a
The gradient of the graph is equal to the
force constant k of the wire. Show that
the force constant k is given by:
k=
EA
l
where E is the Young modulus of the metal,
A is the cross-sectional area of the wire and
l is the natural length of the wire.
[4]
b Explain how the gradient of the force against
extension graph would change for a wire of
the same material but:
i twice the length
[1]
ii twice the radius.
Total:
44
[1]
Score:
%
19
9 Electric current
Intermediate level
1
2
3
State the SI unit for electric charge. [1]
Explain what is meant by electric current. [1]
Name the charged particles responsible for electric current:
a in a metal wire connected to a battery
b in a solution during electrolysis.
[1]
[1]
4
Explain what is meant by conventional current.
[1]
5
Calculate the charge flow at a point in a wire carrying a current of 1.2 A for 3.0
minutes.
[3]
6
Calculate the current for a calculator battery delivering a charge of 3.8 × 10−3 C in
120 s. [3]
7
The current I in a copper wire is given by the equation:
I = Anev
Define all other terms in this equation.
[1]
Higher level
elementary charge e = 1.6 × 10−19 C
8
A solar cell delivers an average current of 80 mA over a 6-hour period. Calculate the
total charge that flows from the solar cell. [3]
9
A resistance wire carries a current of 2.0 A. Calculate the number of electrons flowing
past a point in the wire per second. [3]
10
During a thunderstorm, a lightning strike has a current of 9000 A and transfers a
charge of 18 C to the ground. Calculate:
a the duration of the lightning strike
b the number of electrons transferred to the ground.
[3]
[2]
11
A conducting track on a printed circuit board is 1.5 cm long, 2.5 mm wide and
0.10 mm thick. The current in the track is 150 mA.
a
Suggest why the mean drift velocity of the electrons does not depend on the length of the
track.
b Calculate the mean drift velocity of the electrons in the track. The number density (also
known as the electron density) of the track material is 8.0  1028 m−3.
[1]
[3]
Continued
20
Extension
12
A cell provides a constant current to a circuit. The diagram shows the graph of current
against time.
a Calculate the flow of charge Q in a time t when the current is I.
b Justify the statement: ‘the area under a current against time graph is equal to the charge
flow’.
c Given that the information in b is always true for any graph of current against time,
estimate the total charge delivered by a cell when the current varies as shown in the graph
below.
[1]
[1]
[2]
13
Silicon is a semiconductor. It has fewer free electrons per unit volume than a metal
such as aluminium. A sample of aluminium and a sample of silicon have the same crosssectional area and carry the same current. For electrons in copper and silicon, determine the
following ratio.
ratio 
mean drift velo city in silicon
mean drift velo city in aluminium
Data
number density for aluminium = 6.0  1028 m−3
number density for silicon = 3.0  1018 m−3
Total:
34
Score:
[3]
%
21
10 Resistance and resistivity
Intermediate level
1
Define electrical resistance. [1]
2
State Ohm’s law.
[1]
3
Write a word equation for the resistance of a length of metal wire in terms of the
resistivity of the metal, the length of the wire and its cross-sectional area. [1]
4
A component is connected to a d.c. supply. The supply has negligible internal
resistance.
At 6.0 V, the current in the component is 0.023 A. When the p.d. is doubled, the current in the
component increases to 0.100 A.
a Calculate the resistance of the component at 6.0 V.
b Does the component obey Ohm’s law? Explain your answer.
[2]
[2]
5
The diagram below shows the
I–V characteristics of two components A
and B.
The components are connected in series to a
battery. The current in each component is the
same and equal to 0.60 A.
Calculate the individual resistances of A and B. [2]
6
A 14 m long copper wire of cross-sectional area 4.2 × 10−8 m2 is wound into a coil for
a loudspeaker. The resistivity of copper is 1.7 × 10−8 m. Calculate the resistance of the wire.
[3]
Higher level
7
The diagram shows a thermistor connected to a d.c. supply.
The supply has negligible internal resistance. When the switch S is closed, the current I in the
circuit changes as shown in the graph on the right.
a
Explain why the current changes in the manner shown in the graph.
minimum resistance of thermistor
b Calculate the ratio
maximum resistance of thermistor
[2]
[2]
22
8
The resistance across the ends of a 15 cm long pencil lead is 3.6 . Calculate its radius
given that the pencil lead material has a resistivity of 7.5 × 10−5  m.
[3]
9
A piece of metal is shaped into a rectangular block as shown below.
The metal has a resistivity of 4.3 × 10−4  m.
a
The resistance of the block depends on which pair of faces it is measured between.
Calculate the minimum resistance between two opposite faces of the block.
b What is the maximum current in the block in a when connected to a 0.050 V supply of
negligible internal resistance?
[4]
[2]
10
A filament lamp is connected to a d.c. supply. The current in the lamp is 2.0 A when
the
potential difference across it is 12 V. When operating at 12 V, the filament of the lamp has
a cross-sectional area of 4.9 × 10−9 m2 and the resistivity of the filament material is
5.6 × 10−7  m. Calculate the length of the filament in centimetres. [4]
Extension
11
A glass tube of length 5.0 cm contains a conducting liquid. The internal radius of the
tube is 1.4 cm. The resistivity of the liquid is 8.5 × 10−5  m. The liquid is poured onto a
horizontal surface and quickly sets in the form of a uniform cylindrical disc of radius 25 cm.
Calculate the resistance of this disc across its two opposite larger surfaces. You may assume
that the resistivity of the material remains constant. [4]
12
The resistivity of aluminium is twice that of copper. However, the density of
aluminium is
one-third that of copper.
a
For equal length and resistance, calculate the ratio:
mass of aluminium
mass of copper
[3]
b Use the internet to investigate the construction of power cables used for the National Grid.
You may be surprised to find that the current-carrying cables are made from aluminium
and not copper. Explain why this is so.
Total:
36
Score:
%
23
11 Voltage, energy and power
Intermediate level
1
A cell has an electromotive force (e.m.f.) of 1.5 V. Calculate the chemical energy
transferred when the following charges flow through the cell:
a 1C
b 600 C.
[2]
[1]
2
The potential difference across a filament lamp is 6.0 V. Explain what this means in
terms of energy transfer and charge. [1]
3
Calculate the potential difference across a component that transfers 15 J of energy
when a charge of 4.2 C flows through it.
[2]
4
A 12 V, 36 W lamp is operated for 1 hour (3600 s). Calculate:
a the energy dissipated by the lamp
b the current in the lamp.
5
6
[2]
[2]
Show that 1 kW h is equal to 3.6 MJ. [2]
An electric heater of rating 900 W is operated for a total time of 2.0 hours.
a How much energy is transferred in joules and in kilowatt-hours?
b What is the cost of operating the heater if the cost per kilowatt-hour is 7.5p?
[3]
[2]
Higher level
7
A 100  resistor can safely dissipate 0.25 W. Calculate the maximum current in the
resistor.
[3]
8
A filament lamp in a small torch is labelled as ‘1.5 V, 400 mA’. The filament lamp
transfers 5.0% of the electrical energy into light and the remainder is dissipated as heat.
Calculate:
a the power rating of the lamp
b the power radiated as light
c the resistance of the filament lamp.
9
[2]
[2]
[2]
A 60 W table lamp is operated for a total time of 6.0 hours.
a How much energy is transferred in kW h?
[2]
b For how long can a dishwasher of rating 800 W be operated for the same cost as operating
the 60 W lamp for 6.0 hours?
[2]
24
10
The diagram shows an electrical circuit.
a Calculate the current in lamp X.
b Calculate the ratio:
[2]
resistance of lamp X
resistance of lamp Y
[3]
Extension
11
The coiled filaments in a mains lamp and a car headlamp are made of the same
material and have the same length. Use the information below to calculate the ratio:
cross - sectional area of mains lamp filament
cross - sectional area of headlamp filament
[4]
Mains lamp: 230 V, 100 W Car headlamp: 12 V, 36 W
12
The diagram shows two resistance wires connected in series to a power supply.
The resistance wires have the same length and diameter. The resistivity of nickel is six times
that of iron.
a Which of these two wires will be hotter? Explain your reasoning.
b The two wires are now connected in parallel to the same power supply.
Explain which of these two wires will be hotter.
Total:
45
Score:
[3]
[3]
%
25
12 DC circuits
Intermediate level
1
Two resistors are connected in series to a d.c, supply. The current drawn from the
supply
is 2.0A. What is the current in each resistor? [1]
2
Two identical resistors are connected in parallel. Each resistor has a resistance R.
Determine the total resistance of the combination in terms of R.
3
a
[2]
Calculate the total resistance of each circuit below.
b
c
[1]
[2]
[2]
4
In the electrical circuit shown here,
the battery has e.m.f. 6.0 V and may be
assumed to have negligible internal
resistance.
Calculate:
a the total resistance of the circuit
b the current in each resistor
c the potential difference across the
220  resistor.
[1]
[2]
[2]
Higher level
5
In the parallel circuit shown here, the cell has e.m.f. 1.5
V
and may be assumed to have negligible internal resistance.
Calculate:
a the total resistance of the circuit
b the current shown by the ammeter.
[2]
[2]
6
The diagram shows a number of identical resistors, each of resistance R, connected
between
points A and B.
Determine the total resistance between A and B in terms of R.
[3]
26
7
Light-emitting diodes are easily damaged if the
current in them is too large. To protect a diode
from accidental damage, it must have a ‘safety’
resistor connected in series. The diagram shows
a circuit in which the LED is protected by a
resistor of resistance 100 .
The battery has negligible internal resistance.
Calculate:
a the potential difference across the resistor
b the current in the LED
c the rate of energy supplied by the battery.
[2]
[2]
[2]
8
Six identical lamps are connected in parallel. The power dissipated by each lamp is
60 W and
the total current drawn from the supply is 1.57 A. Calculate:
a the potential difference across each lamp
b the resistance of each lamp.
[3]
[2]
Extension
9
The resistance value of a cheap fixed resistor is often known to an accuracy or
tolerance
of ±10%. Two resistors of resistances 22  and 10 , each having a tolerance of ±10%, are
connected in series to a 12 V d.c. supply of negligible internal resistance.
What are the maximum and minimum values of the current that could be drawn from the
supply?
[4]
10
In circuit calculations, we often assume that a voltmeter has an infinite resistance. In
practice, however, this is not the case. Voltmeters have a finite but high value of resistance.
A student connects up the circuit shown below.
Calculate the reading expected by the student, who presumes that the voltmeter has an infinite
resistance. What is the actual reading on the voltmeter, given that it has a resistance of 220 k?
What effect does the voltmeter have on the circuit?
Total:
40
Score:
[5]
%
27
13 Practical circuits
Intermediate level
1
Suggest why a chemical cell has internal resistance. [1]
2 Use the terms below to write a word equation for the e.m.f. of a power supply.
• terminal p.d.
• e.m.f. of power supply
• p.d. across internal resistance
[1]
a Calculate the current drawn from the supply.
b Suggest why it may be dangerous to have a supply shorted out in this way.
[2]
[1]
3 A d.c. power supply of e.m.f. 12 V has an internal resistance of 2.3 . It is accidentally
shorted
out across its terminals by a short length of wire of negligible resistance.
4
A cell of e.m.f. 1.5 V is connected across a length of wire of resistance 2.6 . A highresistance voltmeter placed across the terminals of the cell measures 0.85 V. Calculate:
a the potential difference across the internal resistance
b the internal resistance of the cell.
5
[2]
[2]
The diagram shows a potential divider circuit.
The battery has negligible internal resistance.
Calculate the potential difference across the 6.0  resistor.
[3]
Higher level
6
A length of wire of resistance 7.3  is connected across the terminals of a cell of
e.m.f. 1.4 V. A high-resistance voltmeter measures a p.d. of 0.81 V across the terminals of the
cell.
Calculate:
a the ‘lost volts’ (the p.d. across the internal resistance of the cell)
b the internal resistance of the cell
power dissipated by the 7.3  wire
c the ratio:
power delivered by the cell
[2]
[2]
[3]
7
Two cells are connected in series. Each cell has e.m.f. 1.4 V and internal resistance
0.38 .
The combination of the cells is connected across an electronic circuit of resistance 1.8 .
Calculate:
a the potential difference across the electronic circuit
b the potential difference across the terminals of each cell.
[4]
[2]
28
8
The diagram shows a potential divider circuit. The voltmeter has infinite resistance
and the
battery has negligible internal resistance.
The variable resistor is set on its maximum resistance of 200 . Calculate the voltmeter
reading.
b The resistance R of the variable resistor is gradually altered from its maximum resistance
value of 200  to zero. Use a sketch graph to describe how the voltmeter reading changes
with R.
a
9 The diagram shows a simple electrical
thermometer based on a negative temperature
coefficient (NTC) thermistor. At 30 °C the
thermistor has a resistance of 2.4 k and this
decreases to 430  at 100 °C. The battery has
negligible internal resistance. Calculate the
maximum input voltage into the datalogger.
[3]
[3]
[4]
Extension
10 A chemical cell has e.m.f. 1.5 V and
internal resistance 0.50 . It is
connected across a variable resistor of
resistance R.
a Copy and complete the table.
(I = current drawn from the cell;
V = terminal p.d.;
P = power dissipated by external
resistor)
b
With the aid of a sketch graph,
describe how the power dissipated
by the external resistor is affected
by its resistance.
R/
I/A
V/V
P/W
0.00
0.10
[2]
0.20
0.30
0.40
0.50
0.60
0.70
0.80
[3]
0.90
1.00
Total:
40
Score:
%
29
14 Kirchoff’s laws
Intermediate level
1
State Kirchhoff’s first law.
[1]
2
Kirchhoff’s first law expresses the conservation of an important physical quantity.
Name the quantity that is conserved.
[1]
3
Determine the current I in each of the circuits below.
a
[1]
b
[1]
c
[2]
4
Several identical cells are used to connect up circuits. Each cell has e.m.f. 1.5 V.
Determine the total e.m.f. for the following combinations of cells.
a
b
c
[1]
5
[1]
[1]
Use Kirchhoff’s second law to calculate the current I in the circuit shown below. [3]
30
Higher level
6 The diagram shows an electrical
circuit. The battery and cell in the circuit
may be assumed to have negligible
internal resistance. Calculate:
a the current in the 12  resistor
[3]
b the p.d. across the 68  resistor. [2]
7
The arrangement below can be used to determine the electromotive force of a test
battery.
The supply battery may be assumed to have negligible internal resistance. The resistance R
of the variable resistor is adjusted until R has a value of 28  and the current shown by the ammeter is
zero. Show that the e.m.f. of the test battery is about 1.1 V.
[3]
Extension
8 Use Kirchhoff’s laws to determine the currents
I1, I2 and I3 in the circuit on the right.
[6]
9 The current measured by the ammeter in the
circuit shown is 0.25 A when the switch S is
open and 0.45 A when the switch is closed.
Use this information to determine the e.m.f.
E and the internal resistance r of the cell.
[6]
Total:
32
Score:
%
31
15 Waves
speed of light in a vacuum c = 3.0 × 108 m s−1
speed of sound in air = 340 m s−1
Intermediate level
1 For a progressive wave, define the following terms:
a
b
c
amplitude
wavelength
frequency.
[1]
[1]
[1]
2 Calculate the frequency of the following waves:
a
b
red light of wavelength 6.5 × 10–7 m emitted from a light-emitting diode
ultrasound of wavelength 7.0 mm emitted by a bat.
[2]
[2]
3 In a water tank, a dipper oscillating at a frequency of 30 Hz produces surface water waves
of wavelength 2.5 cm.
a
b
Calculate the speed of the water waves.
Determine the wavelength of the waves when the frequency of the dipper is doubled.
[2]
[2]
Higher level
4 Displacement against time graphs for two waves A and B of the same frequency are
shown below.
Determine the period and the frequency of the waves.
[2]
5 An oscilloscope has its time base and Y sensitivity (Y gain) set on 0.5 ms cm−1 and
0.5 V cm−1 respectively. A person whistles into a microphone connected to the
oscilloscope. The trace displayed on the oscilloscope screen is shown below.
a Determine the frequency of the sound
wave.
[2]
b Calculate the wavelength of the sound
produced by the whistle.
c Describe how the oscilloscope trace would
change for a louder whistle of half the
frequency of a.
[2]
[2]
32
6
You can use the following equation to determine the intensity of a wave:
power
cross - sectional area
This equation can be applied to all waves, including sound.
intensity 
The intensity of sound at a certain distance from a loudspeaker is 3.5 × 10−3 W m−2.
The amplitude of the sound waves at this point is known to be 0.45 mm. Calculate:
the power transmitted through a cross-sectional area of 8.0 × 10−5 m2 when the intensity
of sound is 3.5 × 10−3 W m–2
b the intensity of sound where the amplitude is 0.90 mm
c the amplitude of the sound waves where the intensity is 5.6 × 10−2 W m−2.
a
[2]
[3]
[3]
Extension
7
The intensity of a wave may be defined as the power transmitted per unit crosssectional area at right angles to the direction of travel.
a
For a point source of light, explain why the intensity I at a distance r away from the source
obeys an inverse square law with distance, that is:
1
[3]
I 2.
r
b The intensity of visible light from the Sun reaching the upper parts of our atmosphere is
about 1.4 kW m−2. The Sun has a radius of 7.0 × 108 m and is 1.5 × 1011 m from the Earth.
Calculate:
i the intensity of visible light emitted from the Sun’s surface
[3]
ii the total power radiated by the Sun in the visible region of the electromagnetic spectrum [2]
iii the intensity of light from the Sun at the planet Neptune. (Neptune is 4.5 × 1012 m from
the Sun.)
[3]
Total:
38
Score:
%
33
16 Electromagenetic waves
speed of light in a vacuum c = 3.0 × 108 m s−1
Intermediate level
1 a State two common properties of all the waves in the electromagnetic spectrum.
b State one main difference between X-rays and sound waves.
[2]
[1]
2
Complete the table below, naming the electromagnetic radiation with each specified
wavelength. [3]
Wavelength/m
2 × 10−10
4.5 × 10−2
2.5 × 103
Name of radiation
3
A television remote control emits infrared radiation of wavelength 8.5 × 10−7 m.
Calculate:
a the frequency of this infrared radiation
b the distance travelled by the infrared radiation in a time of 0.20 s.
4 Explain what is meant by plane polarised light.
[2]
[2]
[1]
5
Visible light and microwaves can be polarised. What can be deduced about the nature
of
these two waves?
[1]
6
Two types of ultraviolet radiation reaching the Earth’s surface are UV-A and UV-B.
a What does UV-A do to our skin?
b State one advantage and one disadvantage of exposure to UV-B.
[1]
[2]
Higher level
7 a Give typical values for the wavelength of X-rays and of -rays.
b Use your values in a to determine the ratio:
frequency of  - rays
ratio =
frequency of X - rays
[2]
[2]
8
Astronomers detect intense electromagnetic radiation of frequency 300 GHz coming
from all directions of the sky as evidence of the Big Bang. Determine the wavelength of this
radiation,
and hence name the region of the electromagnetic spectrum where this radiation may be
detected.
[3]
9
Describe how you can show that reflected light from a shiny surface such as glass is
(partially) polarised. [2]
10 a State Malus’s law.
[1]
b Vertically polarised light is incident on a polaroid whose axis is at 30° to the vertical.
The incident intensity of light is 0.48 W m−2. Calculate the intensity of the transmitted light
through the polaroid.
[3]
34
Extension
11
Our modern society relies heavily on communication using radio waves. Radio waves
generated by a transmitter have to propagate through the atmosphere, and sometimes empty
space, in order to reach the receiver. Depending on their frequency, there are three modes
(methods) by which they reach their destination: as surface waves, sky waves or space waves.
Use the internet to find the frequencies and some of the characteristics of these waves.
Total:
28
Score:
%
35
17 Superposition of waves
speed of light in a vacuum c = 3.0 × 108 m s−1
Intermediate level
1
State the principle of superposition of waves.
[1]
2 a Describe what is meant by the diffraction of a wave.
b Electromagnetic radiation of frequency 7.5 × 109 Hz is directed towards a slit
of width 6.0 cm.
i Determine the wavelength of the radiation.
ii Explain whether or not the radiation will be diffracted at the slit.
3
4
B.
[1]
[2]
[1]
Explain what is meant by coherent sources. [1]
The diagram below shows the displacement against time graphs for two waves A and
a What is the phase difference between the two waves?
b The two waves A and B are combined. Name the type of interference that will occur.
[1]
[1]
5The diagram below shows an arrangement used to demonstrate the interference of water
waves.
a
Constructive interference occurs at point A. What is the path difference of the waves from
the gaps S1 and S2?
[1]
b The water waves have a wavelength of 3.0 cm. Determine the path difference for
the waves arriving at point B. Name the type of interference taking place at this point.
[3]
6
A two-slit arrangement is used to determine the wavelength  of light. The wavelength
is
given by the equation:
ax
D
Define the terms in the equation above.
=
[3]
36
Higher level
7
A microwave source is directed towards a metal plate with two narrow vertical slits. A
receiver is slowly moved along the line XY as shown in the diagram.
a Explain why the receiver registers a series of maxima and minima.
b The wavelength of the microwaves is 2.8 cm. The separation between the slits is 4.0 cm
and the receiver is a distance of 80 cm from the slits. Calculate the separation between
adjacent maxima.
c Describe the effect on your answer to b when:
i the separation between the slits is halved
ii the distance between the slits and the receiver is doubled.
[3]
[3]
[1]
[1]
8
Monochromatic light is incident normally at a diffraction grating with 60 lines per
mm.
The tenth-order maximum is observed at an angle of 19°. Determine:
a the spacing (in metres) between the centres of the adjacent lines
b the wavelength of incident light.
[2]
[3]
9
Yellow light of wavelength 5.5 × 10−7 m is incident normally at a diffraction grating
with
300 lines per mm. Calculate the angle between the first-order and second-order maxima. [5]
10
Blue light of wavelength 4.5 × 10−7 m is incident normally at a diffraction grating with
100 lines per mm. Calculate the maximum number of orders that can be observed. [4]
Extension
11
Answer the following questions with supporting calculations.
You are given a diffraction grating with 40 lines per mm.
The diffraction grating is mounted on an instrument that can measure angles to within 0.1°.
Can this instrument be used to determine the individual wavelengths of spectral lines of
wavelengths 589.6 nm and 589.0 nm?
[6]
b White light is incident normally at the grating. Estimate the angle between the extreme
ends of the spectrum for the tenth-order maxima.
[4]
a
Total:
47
Score:
%
37
18 Stationary waves
Intermediate
1
One end of a rope is fixed and the other end is shaken rhythmically. A stationary
(standing)
wave is formed on the rope. Explain how such a wave is formed on the rope.
[2]
2
Complete the table below that compares progressive and stationary waves.[4]
Progressive wave
Stationary wave
Energy is transferred from one point to
another in the direction of wave travel.
There are some points that always have
zero displacement or amplitude.
There is a phase difference between
adjacent points of the wave.
All points have the same amplitude.
3
The diagram below shows a stationary wave on a string.
a Mark the positions of the nodes (N) and the antinodes (A).
[2]
b Explain what is meant by a node and an antinode.
[2]
c The stationary wave in the diagram above is drawn to scale. Use a ruler and this pattern to
determine the wavelength  of the progressive waves on the string.
[3]
4
A string of length 80 cm is fixed at both ends. The middle of the string is plucked.
This creates
a stationary wave pattern on the string with one complete ‘loop’. The string is vibrating in
fundamental mode with a frequency of 20 Hz. Calculate:
a the wavelength of the progressive wave on the string
b the speed of the progressive wave on the string.
[2]
[3]
Higher
5
A tuning fork vibrating at a frequency of 490 Hz is held above the open end of an
empty bottle. When the length of the air column within the bottle is 17 cm, a fundamental
mode of vibration
is set up in the air within the bottle and a loud sound is heard.
a
Sketch a diagram of the stationary wave pattern. (Assume the air within the bottle is a
uniform cylinder of air.)
b Determine the wavelength of the sound waves.
c Hence determine the speed of sound in air.
[2]
[2]
[3]
38
6
A string of length 1.6 m is held under tension. When the string is made to vibrate at a
frequency
of 400 Hz, three antinodes are formed along this length of the string. Determine the speed of
progressive waves that form the stationary wave pattern. [5]
7 The diagram below shows a stationary wave pattern formed in the air between the open
ends
of a tube when a vibrating loudspeaker is held at one end. The positions of the nodes (N)
and antinodes (A) are also shown.
The length L of the tube is 60 cm. The speed of sound is 340 m s−1.
Determine the frequency of sound from the loudspeaker.
[5]
Extension
8
In a resonance-tube experiment, a tuning fork
vibrating at
a frequency of 256 Hz is held over the open end of a tube
(as shown in the diagram).
A stationary wave can form in the air between the open end of
the tube and the surface of the water. The antinode at the open
end of the tube does not occur exactly at the end but at a small
distance c from this end. The distance c is known as the ‘endcorrection’. The value of c for a particular tube does not
depend on the harmonic.
This experiment takes into account any errors that may occur
due to the end-correction. The tube is fully immersed into the
water. The open end of the tube is slowly raised. A loud
sound is first heard when the top of the tube is 30 cm above
the surface of the water. The next loud sound is heard when the top of the tube is 95 cm above the
water surface.
Use this information to determine the speed of sound in air.
[6]
Total:
41
Score:
%
39
19 Quantum physics
Planck constant h = 6.63 × 10−34 J s
speed of light in a vacuum c = 3.0 × 108 m s−1
mass of electron me = 9.1 × 10−31 kg
mass of neutron = 1.7 × 10−27 kg
elementary charge e = 1.6 × 10−19 C
Intermediate level
1
What is a photon?
[1]
2
-rays from a radioactive material have higher frequency than visible light.
Explain why this means that -rays are more harmful.
[2]
3
State one piece of evidence that electromagnetic radiation has:
4
a wave-like properties
b particle-like properties.
[1]
[1]
a the frequency of the red light
b the energy of a photon of red light.
[2]
[3]
A light-emitting diode emits red light of wavelength 6.4 × 10–7 m. Calculate:
5
Using the terms photons and work function, describe why electrons are emitted from
the
surface of a zinc plate when it is illuminated by ultraviolet radiation but not when it is
illuminated by visible light. [3]
6
What experimental evidence is there that suggests that electrons behave as waves? [1]
Higher level
7
The electronvolt is a convenient unit of energy for particles and photons. Define the
electronvolt. [1]
8
An electron is accelerated through a potential difference of 6.0 V. According to a
student, this electron has kinetic energy much greater than the energy of a photon of
ultraviolet radiation of wavelength 2.5 × 10–7 m. With the aid of calculations, explain whether
or not the student is correct. [5]
9 a Define threshold frequency for a metal.
b The work function of caesium is 1.9 eV. Calculate the threshold frequency.
[1]
[3]
10
A particular filament lamp of rating 60 W emits 5.0% of this power as visible light.
The average wavelength of visible light is 550 nm. Calculate:
a the average energy of a single photon of visible light
b the number of photons of visible light emitted per second from the lamp.
[3]
[3]
11
A plate of zinc is illuminated by electromagnetic radiation of wavelength 2.1 ×
10−7 m.
The work function of zinc is 4.3 eV. Calculate the maximum kinetic energy of a
photoelectron. [4]
12
Neutrons travelling through matter get diffracted just as electrons do when travelling
through graphite. In order to show diffraction effects, the neutrons need to have a de Broglie
wavelength that is comparable to the spacing between the atoms.
Calculate the speed of a neutron that has a de Broglie wavelength of 2.0 × 10−11 m.
[3]
40
13
A yellow light-emitting diode (LED) is connected to a d.c. power supply. The output
voltage
from the supply is slowly increased from zero until the LED just starts to glow. The yellow
light from the LED has a wavelength of about 5.8 × 10−7 m. Estimate the potential difference
across the LED when it just starts to glow. [4]
Extension
14 a
In an electron-diffraction experiment, electrons are accelerated through a p.d. V.
Show that the de Broglie wavelength  of an electron is given by:
h
=
2meeV
where me is the mass of the electron and e is the elementary charge.
b Calculate the accelerating p.d. V that gives an electron a de Broglie wavelength of
4.0 × 10−11 m.
[3]
[3]
15
In an experiment on the photoelectric effect, a metal is illuminated by visible light of
different wavelengths. A photoelectron has a maximum kinetic energy of 0.9 eV when red
light of wavelength of 640 nm is used. With blue light of wavelength 420 nm, the maximum
kinetic energy of the photoelectron is 1.9 eV. Use this information to calculate an
experimental value
for the Planck constant h.
[5]
Total:
52
Score:
%
41
20 Spectra
speed of light in a vacuum c = 3.0 × 108 m s−1
Planck constant h = 6.63 × 10−34 J s
1 eV = 1.6 × 10−19 J
Intermediate level
1
The figure below shows an electron making a transition between two energy levels
and the bright spectral emission line observed.
a
Explain why electromagnetic radiation is emitted when an electron jumps from
energy level E1 to energy level E2.
b Derive an expression for the frequency f of the radiation emitted.
c State and explain the position of the spectral line when an electron makes a transition
between energy levels E1 and E3.
[2]
[2]
[2]
2
An electron in an atom can occupy four energy levels. With the help of an energy level
diagram, determine the maximum number of spectral emission lines from this atom.
[2]
3
Lithium atoms emit red light of wavelength 670 nm. Calculate the difference between
the
energy levels responsible for this red light. [3]
4
The diagram below shows a hot solid, at a temperature of 5000 K, emitting a
continuous
spectrum.
State the type of spectrum observed from:
a position X
b position Y
c position Z.
[1]
[1]
[1]
42
Higher level
5
The diagram below shows the some of the energy levels for a helium atom.
a Explain the significance of the energy levels being negative.
b When a helium atom is not excited, the electrons have an energy of −3.00 eV. This is
known as the stable state of the electrons. Calculate the minimum energy, in joules,
required to free an electron at this energy level. Explain your answer.
c The helium atom absorbs a photon of energy 1.41 eV.
i State the transition made by an electron.
ii Calculate the wavelength of the radiation absorbed by the helium atom.
[1]
[3]
[2]
[3]
6
The figure below
shows the energy level
diagram for an atom of
mercury.
a Explain what is meant by the ground state.
b Calculate the shortest wavelength
emitted by the atom. Explain your
answer.
[4]
[1]
Extension
7
For the hydrogen atom, the energy level En in joules is given by the equation
En  
2.18 10 18
n2
where n is an integer, known as the principal quantum number.
a
Calculate the energy level of the ground state (n = 1) and the energy level of the first
excited state (n = 2).
b Determine the wavelength of radiation emitted when an electron makes a transition from
the first excited state to the ground state. In which region of the electromagnetic spectrum
would you find a spectral line with this wavelength?
c In which region of the electromagnetic spectrum would you find the spectral line
corresponding to an electron transition between energy levels with principal quantum
numbers of 6 and 7? Justify your answer.
Total:
38
Score:
[2]
[4]
[4]
%