Synoptic Exam Questions (Paper 1 & 2) (AQA A Level Physics): Exam Questions

The core of a thermal nuclear reactor contains a number of components that are exposed to moving neutrons. 

State what happens to a neutron that is incident on: 

• the moderator

• a control rod.

A slow-moving neutron collides with a nucleus of an atom of the fuel which induces nuclear fission. 

Describe what happens in the process of induced fission.

A student sets up the arrangement, shown in Figure 8, to demonstrate the principle of moderation in a nuclear reactor.

Figure 8

A golf ball of mass $m$ is initially hanging vertically and just touching a hockey ball of mass $3m$. The golf ball is pulled up to the side and released. After the collision, the balls move in opposite directions with equal speeds.

Explain, with numerical detail, how this arrangement demonstrates the moderation process in a reactor.

A thermal nuclear reactor produces radioactive waste.

State the main source of the most dangerous waste and describe one problem faced in dealing with the waste.

Thin films of carbon are sometimes used in electronic systems. 

Typical dimensions of such a film are shown in Figure 7.

Figure 7

Calculate the current which passes through the carbon film shown in Figure 7 for an applied voltage of 2.5 mV. 

The resistivity of carbon = 4.0 × 10^–5 Ω m

The applied voltage is kept constant, but the current is now directed through the carbon film as shown in Figure 8.

Figure 8

Show that the current is approximately 6 magnitudes larger when directed through the carbon film, as shown in Figure 8.

A tensile force is applied to the carbon film in Figure 8 in a plane that is normal to the current. 

Without performing any calculations, state and explain how the resistance of the carbon film changes as a result of the applied tensile force, stating one assumption you make.

The International Space Station (ISS) orbits travels around the Earth once every 93 minutes. 

Calculate the angular speed of the ISS.

Calculate the distance of the ISS above the Earth’s surface.

The Soyuz is a Russian spacecraft that carries astronauts to and from the international space station (ISS). The ISS has a mass of approximately 4.2 × 10⁵ kg. 

Calculate the change in kinetic energy of a Soyuz travelling from the Earth’s surface to the ISS.

Without performing any further calculations, explain how the change in kinetic energy relates to the change of the potential energy when the Soyuz travels from the Earth’s surface to the ISS. 

Cyclotrons are used to accelerate particles, such as protons, for a number of applications. 

A cyclotron has two D-shaped regions called ‘dees’ where the magnetic flux density is constant. The dees are separated by a small gap. An alternating electric field between the dees accelerates charged particles. The magnetic field causes the charged particles to follow a circular path. 

Figure 5 shows the path followed by a proton that starts from O.

 Figure 5

State the direction the magnetic field acts over the dees in Figure 5.

Explain why it is not possible for the magnetic field to alter the speed of a proton while it is in one of the dees.

Show that the time taken by a proton to travel around one semi-circular path is independent of the radius of the path.

The maximum radius of the path followed by the proton is 0.46 m and the magnetic flux density of the uniform field is 0.88 T. 

Calculate the maximum speed of a proton when it leaves the cyclotron. 

Ignore any relativistic effects.

The protons leave the cyclotron when the radius of their path is equal to the outer radius of the dees. 

Determine the radius required for the cyclotron to produce protons with a maximum kinetic energy of 25 MeV. 

Ignore any relativistic effects.

A student investigates the refraction of light using a semicircular glass block. The refractive index of the glass is 1.52.

State the two conditions required for total internal reflection to occur at a boundary.

A ray of light strikes the flat surface of the block at an angle of 50° to the normal, as shown in Figure 2.

Figure 2

Complete, on Figure 2, the path of the ray of light.

Support your answer with a suitable calculation.

The flat surface of the glass block is now placed in contact with water.

Explain how the student could use the glass block to measure the refractive index of water.

The student then uses a diffraction grating to analyse the light from a sodium lamp. The sodium lamp emits two closely spaced wavelengths known as the sodium doublet:

${\lambda }_1=589.0\text{ nm}{\lambda }_2=589.6\text{ nm}$

The diffraction grating has 600 lines per mm.

Calculate the angle of diffraction for the second-order maximum of ${\lambda }_1$.

The student wants to resolve the sodium doublet and is considering two options:

• Option 1: observe the second-order spectrum ($n=2$) using the original 600 lines per mm grating

• Option 2: observe the first-order spectrum ($n=1$) using a different grating with 1200 lines per mm

Discuss which option the student should choose.

Figure 4 shows part of a circuit used to detect temperature changes.

A fixed resistor of resistance $2.5\mathrm{\Omega }$ is connected in series with a thermistor of resistance $12\mathrm{\Omega }$ at room temperature. The battery has an emf of $6.0\mathrm{V}$ and an internal resistance of $0.50\mathrm{\Omega }$.

Figure 4

Calculate the current in the circuit.

Calculate the expected reading on the voltmeter.

The actual voltmeter reading is 4.6 V.

Suggest one reason for the difference between the expected and actual readings.

The fixed resistor is made from a wire of length $0.80\mathrm{m}$ and diameter $0.28\mathrm{mm}$.

Calculate the resistivity of the wire.

The thermistor is heated so that its resistance decreases to $3.0\mathrm{\Omega }$. A warning LED is to be connected in parallel with either the fixed resistor or the thermistor. The LED illuminates when the potential difference across it exceeds $2.0\mathrm{V}$.

Determine which component the LED should be connected across so that it acts as a high-temperature warning. Support your answer with calculations.

A turntable rotates at a constant angular speed. A small block of mass $0.050\mathrm{kg}$ is placed on the turntable at a distance of $0.12\mathrm{m}$ from the centre, as shown in Figure 6.

Figure 6

The block is on the verge of sliding when the turntable completes one revolution every $0.85\mathrm{s}$.

Calculate the angular speed of the turntable.

Show that the frictional force acting on the block is approximately $0.3\mathrm{N}$.

The block is now moved to a distance of $0.20\mathrm{m}$ from the centre. The turntable continues to rotate at the same angular speed. The maximum frictional force between the block and the turntable surface does not change.

Determine whether the block will slide at this new position.

The block is placed on a horizontal platform that is attached to a vertical spring, as shown in Figure 7. The platform oscillates vertically with simple harmonic motion. At a frequency of $2.5\mathrm{Hz}$, the mass just loses contact with the platform at the highest point of the oscillation when the amplitude is $0.040\mathrm{m}$.

Figure 7

Suggest the condition required for the mass to lose contact with the platform at the highest point.

Calculate the maximum amplitude at a frequency of $4.0\mathrm{Hz}$ for which the block remains in contact with the platform throughout the oscillation.

State what is meant by the internal energy of an ideal gas.

A sealed glass flask of volume $0.020{\text{ m}}^3$ contains air at $27°\mathrm{C}$. The pressure of air in the flask is $1.5\times {10}^5\text{ Pa}$.

Calculate the number of molecules of air in the flask.

Explain, using the kinetic theory model, why the pressure of an ideal gas increases when it is heated at constant volume.

The temperature of the air is increased from $27°\mathrm{C}$ to $127°\mathrm{C}$.

Calculate the change in the mean kinetic energy of a molecule of air in the flask.

When an ideal gas is heated at constant volume, all of the energy supplied by heating is used to increase the mean kinetic energy of the particles.

When air is heated at constant volume, its specific heat capacity is $720{\text{ J kg}}^{-1}{\text{ K}}^{-1}$.

Deduce whether air behaves as an ideal gas when heated at constant volume.

molar mass of air = $2.9\times {10}^{-2}{\text{kg mol}}^{-1}$

An isolated solid conducting sphere of radius $0.10\text{ m}$ is positively charged.

Figure 1 shows how the electric potential $V$ varies with distance $r$ from the centre of the sphere.

Figure 1

Determine the magnitude of the electric field strength at a distance of $0.20\text{ m}$ from the centre of the sphere.

State an appropriate SI unit for your answer.

The sphere acts as a capacitor because it stores charge at an electric potential.

Show that the capacitance of the sphere is approximately $1\times {10}^{-11}\text{ F}$.

The charged sphere momentarily touches an identical uncharged conducting sphere. The two spheres are then separated.

Explain why the total energy stored by the two spheres after separation is less than the energy stored by the single sphere before contact.

Two stable isotopes of helium are ${}_2{}^4\text{He}$ and ${}_2{}^3\text{He}$.

An atom of ${}_2{}^4\text{He}$ is produced in a rock that contains uranium. It is produced following the radioactive decay of a ${}_{92}{}^{238}\text{U}$ atom. The decay also creates an atom of thorium (Th).

Write an equation for the decay of ${}_{92}{}^{238}\text{U}$.

${}_{92}{}^{238}\text{U}\to$ ....................................................................

A ${}_2{}^3\text{He}$ nucleus can be produced by the decay of a tritium nucleus ${}_1{}^3\text{H}$.

State and explain which exchange particle is responsible for this decay.

Helium was discovered by analysing the light in the absorption spectrum of the Sun.

Figure 1 shows the positions of the brightest lines, labelled A to F, in the emission spectrum of helium. The brightest lines in the emission spectra of sodium and hydrogen are also shown.

Figure 1

Before helium was identified, some scientists suggested that the lines of the helium spectrum seen in the absorption spectrum of the Sun were due to the presence of sodium and hydrogen.

Discuss, with reference to the lines A to F in Figure 1, the evidence for and against this suggestion.

Calculate, in eV, the change in energy level responsible for the spectral line labelled E in Figure 1.

change in energy level = .................................... eV

Explain, with reference to the processes within an atom, the difference between an emission spectrum and an absorption spectrum.

Figure 3 shows a garden gate with a pulley system designed to close the gate.

Figure 3

The pulley system raises weight A when the gate is opened. When the gate is released, A falls. The horizontal cable C passes over pulley R. The tension in cable C causes the gate to close.

Weight A is a solid cylinder with the following properties:

diameter = $4.8\times {10}^{-2}\text{ m}$
length = $0.23\text{ m}$
weight = $35\text{ N}$

Table 2 gives the density of three available materials.

Table 2

Deduce which one of the three materials is used for A.

Figure 4 shows the pulley arrangement when the gate is closed.

Figure 4

Pulleys P and M are frictionless so that the tension in the rope attached to A is equal to the weight of A.

A weighs $35\text{ N}$ and the weight of moveable pulley M is negligible.

Calculate the tension in the horizontal cable C when the gate is closed.

tension = .................... N

Pulley M is pulled to the left as the gate is opened.

Explain why this increases the tension in the horizontal cable C.

Figure 5 shows a plan view with the gate open. The horizontal cable C passes over pulley R and is attached to the door at D.

The angle between the door and the horizontal cable C is $12°$.

The horizontal distance between the hinge and D is $0.95\text{ m}$.

Figure 5

The tension in the horizontal cable C is now $41\text{ N}$.

Calculate the moment of the tension about the hinge.

moment = .................... N m

The same system is attached to an identical gate with stiffer hinges. Now the system does not supply a sufficiently large moment to close the gate.

Discuss two independent changes to the design to increase the moment about the hinges due to horizontal cable C.

Cosmic rays are high-energy particles that come from space. Most of these particles are protons. There are other particles in cosmic rays, including atomic nuclei.

Table 1 gives the data for one particular nucleus X.

Table 1

Determine the number of neutrons in nucleus X.

number of neutrons = ....................

Calculate the speed of X.

Ignore relativistic effects.

speed = .................... m s^-1

A pion (${\mathrm{\pi }}^{+}$) and a kaon (${\text{K}}^{+}$) are produced when cosmic rays interact with the upper atmosphere.

The ${\mathrm{\pi }}^{+}$ decays to produce a positron and an electron neutrino.

Show how the conservation laws apply to this decay.

The ${\text{K}}^{+}$ decays to produce an anti-muon and a muon neutrino.

Explain how strangeness applies in this decay.

Write an equation for a ${\text{K}}^{+}$ decay that involves only hadrons.

Figure 6 shows a rotating spacecraft that is proposed to carry astronauts to Mars.

Figure 6

The spacecraft consists of two parts A and B connected by a rigid cylindrical rod.

When the spacecraft is travelling, A and B rotate at a constant angular speed about their common centre of mass O.

$L$ is the distance between the centre of mass of A and the centre of mass of B.

$r_{\text{A}}$ is the distance from O to the centre of mass of A.

As the spacecraft rotates, a force that imitates the effect of gravity acts on an astronaut who is in contact with the floor.

Explain why.

The forces exerted on A and B by the connecting rod have the same magnitude.

$m_{\text{A}}$ is the mass of A

$m_{\text{B}}$ is the mass of B

Show, by considering the centripetal forces acting on A and B, that $r_{\text{A}}$ is given by

$r_{\text{A}}=\frac{m_{\text{B}}L}{m_{\text{A}}+m_{\text{B}}}$

In this spacecraft $m_{\text{A}}<m_{\text{B}}$.

Deduce whether the centre of mass of A or the centre of mass of B rotates with a greater linear speed.

The astronauts live in A and the cargo is stored in B.

When loaded,

$m_{\text{A}}=1.32\times {10}^6\text{ kg}$

$m_{\text{B}}=3.30\times {10}^6\text{ kg}$.

The spacecraft imitates the gravity of Mars where $g=3.7{\text{ m s}}^{-2}$.

Figure 7 shows a stress–strain curve for the metal used for the rigid rod.

Figure 7

Suggest a suitable diameter for the rod.

Justify your answer.

diameter = .................... m

Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres.

The spheres are suspended by non-conducting thread.

Figure 3

Each sphere has a mass of $3.2\times {10}^{-3}\text{ kg}$ and a radius of $20\text{ mm}$.

The distance d is $40\text{ mm}$.

The capacitance of a sphere of radius r is $4\pi {ϵ}_{0}r$.

Each sphere is charged by connecting it briefly to the positive terminal of a high-voltage supply, the other terminal of which is at $0\text{ V}$.

After this has been done the charge on each sphere is $52\text{ nC}$.

Calculate the potential of one of the spheres.

potential = .................... V

The charged spheres in Figure 3 are at equilibrium.

Draw labelled arrows on Figure 3 to show the forces on sphere B.

Suggest a solution to one problem involved in the measurement of d in Figure 3.

Show that the magnitude of the electrostatic force on each sphere is about $4\times {10}^{-3}\text{ N}$.

A student measures the angle θ when the apparatus in Figure 3 is at equilibrium.

The student records θ as 7°.

Discuss whether this measurement is consistent with the other data in this investigation.

The student says that the gravitational force between the two spheres has no significant effect on the angle at which the spheres are in equilibrium.

Deduce with a calculation whether this statement is valid.

Ions orbit Jupiter in a ring called a plasma torus as shown in Figure 6.

This question is about applying gravitational, magnetic and electric fields to a particle in the plasma.

Figure 6

An ion travels in a circular path at a speed of $74.2{\text{ km s}}^{-1}$ and at a distance of $4.22\times {10}^8\text{ m}$ from the centre of Jupiter.

Student A suggests that the gravitational force acting on the ion due to Jupiter provides the centripetal acceleration of the ion.

Deduce whether this suggestion is correct.

mass of Jupiter = $1.90\times {10}^{27}\text{ kg}$

Student B suggests that the magnetic field of Jupiter alone can cause the ion to move in the circular path.

Figure 7 shows the direction of the velocity v of the ion in the plasma torus.

v is tangential to the plasma torus.

Figure 7

The ion has a positive charge.

Student B's suggestion requires a magnetic field to act at the position of the ion.

Draw an arrow on Figure 7 to show the direction of this magnetic field.

The ion has a charge of $+3.20\times {10}^{-19}\text{ C}$ and a mass of $5.31\times {10}^{-26}\text{ kg}$.

The ion moves with a speed of $74.2{\text{ km s}}^{-1}$ in a circle of radius $4.22\times {10}^8\text{ m}$.

Calculate the magnitude of the magnetic flux density required for this motion.

State, in fundamental (base) units, the unit for your answer.

Ignore any contribution from the gravitational field.

magnetic flux density = .................... unit = ....................

An electric field of strength $371{\text{ μV m}}^{-1}$ can also accelerate the ion.

Calculate the acceleration of the ion due to this electric field.

acceleration = .................... m s^-2

The plasma torus contains two ions X and Y as shown in Figure 8.

X has a charge of $+2e$.

Y has a charge of $+1e$.

Assume that each ion acts as a point charge.

Figure 8

Calculate the magnitude of the resultant electric field strength at point P in Figure 8 due to the two ions.

resultant electric field strength = .................... V m^-1

A radioisotope thermoelectric generator (RTG) uses radioactive decay to generate electrical energy.

A vehicle that is used to examine the surface of Mars includes an RTG that initially contains $3.23\times {10}^{24}$ atoms of plutonium-238 $\left({}_{94}{}^{238}\text{Pu}\right)$.

Determine the initial mass of plutonium-238 in the RTG.

initial mass = .................... kg

The plutonium-238 undergoes alpha decay.

The energy released by this decay is converted into electrical energy with an efficiency of $4.58\%$.

The power provided by the RTG decreases over time as the plutonium-238 decays.

The vehicle requires a minimum electrical power of $29.6\text{ W}$ to operate.

Calculate the initial activity of the plutonium-238.

Go on to determine, in Earth years, the time for which the RTG can provide sufficient power for the vehicle to operate.

decay constant of plutonium-238 $=2.51\times {10}^{-10}{\text{ s}}^{-1}$

energy of alpha particle emitted by plutonium-238 $=8.94\times {10}^{-13}\text{ J}$

initial activity = .................... Bq

time = .................... Earth years

The vehicle has a battery-powered laser that is used to vaporise small samples of ice.

On Mars, ice changes directly from solid to vapour at a temperature of $0\text{ °C}$.

The ice does not form a liquid.

The energy required to vaporise $1.0\text{ g}$ of solid ice directly into water vapour is the same as the total energy required to melt $1.0\text{ g}$ of ice and then to vaporise the melted ice.

The laser produces an output power of $1.0\text{ kW}$ for a maximum time of $3.0\text{ s}$ before its battery needs to be recharged.

The laser heats the ice from an initial temperature of $-25\text{ °C}$ to a temperature of $0.0\text{ °C}$. The laser then transfers energy to vaporise the ice at $0.0\text{ °C}$.

Determine whether the laser is able to vaporise $1.0\text{ g}$ of the ice that is initially at $-25\text{ °C}$ before the battery needs to be recharged.

specific heat capacity of ice $=2.1{\text{ kJ kg}}^{-1}{\text{ K}}^{-1}$

specific latent heat of fusion of ice $=334{\text{ kJ kg}}^{-1}$

specific latent heat of vaporisation $=2500{\text{ kJ kg}}^{-1}$

Figure 11 shows alpha particles all travelling in the same direction at the same speed.

The alpha particles are scattered by a gold (${}_{79}{}^{197}\text{Au}$) nucleus.

The path of alpha particle 1 is shown.

Figure 11

State the fundamental force involved when alpha particle 1 is scattered by the nucleus in Figure 11.

Draw an arrow at position X on Figure 11 to show the direction of the rate of change in momentum of alpha particle 1

Suggest one of the alpha particles in Figure 11 which may be deflected downwards with a scattering angle of $90°$

Justify your answer.

alpha particle number = ....................

Alpha particle 4 comes to rest at a distance of $5.5\times {10}^{-14}\text{ m}$ from the centre of the ${}_{79}{}^{197}\text{Au}$ nucleus.

Calculate the speed of alpha particle 4 when it is at a large distance from the nucleus.

Ignore relativistic effects.

mass of alpha particle $=6.8\times {10}^{-27}\text{ kg}$

speed = .................... m s^-1

The nuclear radius of ${}_{79}{}^{197}\text{Au}$ is $6.98\times {10}^{-15}\text{ m}$.

Calculate the nuclear radius of ${}_{47}{}^{107}\text{Ag}$.

radius = .................... m

All nuclei have approximately the same density.

State one conclusion about the nucleons in a nucleus that can be deduced from this fact.

Figure 4 and Figure 5 show apparatus used in an experiment to confirm the distribution of atom speeds in a gas at a particular temperature.

The oven contains an ideal gas kept at a constant temperature. Atoms of the gas emerge from the oven and some pass through the narrow slit S in a rapidly rotating drum. The drum is in a vacuum.

Explain why the drum must be in a vacuum.

One atom leaves the oven, enters the drum through S and travels in a straight line across the drum.

In the time taken for the atom to move from S to the detector AB, the drum rotates through 45°. The atom hits the detector at point C, as shown in Figure 5.

drum diameter = distance from S to A = $0.500\text{ m}$

drum rotational speed = $120$ revolutions per second

Show that the atom is moving at a speed of about $500{\text{ m s}}^{-1}$.

The speed of the atom in part (b) is equal to $c_{\text{rms}}$, the root mean square speed of the atoms of the gas in the oven.

The molar mass of the gas is $0.209{\text{ kg mol}}^{-1}$.

Calculate the temperature of the gas in the oven.

temperature = .................... K

The oven temperature is kept constant during the experiment but the pressure in the oven decreases as atoms leave through the exit hole.

Explain, using the kinetic theory, why the pressure decreases.

The pressure of gas in the oven is initially $5.0\times {10}^4\text{ Pa}$.

The volume of the oven is $2.7\times {10}^{-2}{\text{ m}}^3$.

During the experiment the pressure in the oven decreases to $4.5\times {10}^4\text{ Pa}$.

Calculate, in mol, the amount of gas that has emerged from the oven.

amount of gas = .................... mol

Atoms enter the drum every time S passes the exit hole. The detector darkens at the point where an atom strikes it.

After a time, the detector is removed from the drum.

Figure 6 shows the appearance of the detector.

Figure 6

A new detector is placed in the drum and the experiment is repeated with a new sample of the same gas at a higher temperature.

Describe and explain the appearance of this detector when the experiment is repeated.

Figure 6 shows an oscilloscope connected across resistor R which is in series with an ac supply. The supply provides a sinusoidal output of peak voltage $15\text{ V}$.

Figure 6

Calculate the rms voltage of the supply.

rms voltage = .................... V

Figure 7 shows the trace of the waveform displayed on the oscilloscope.

Figure 7

Determine the y-voltage gain of the oscilloscope used for Figure 7.

y-voltage gain = .................... V div^-1

A dc supply gives the same rate of energy dissipation in R as the ac supply in Figure 6.

Draw the trace of the output of the dc supply on Figure 7.

The oscilloscope settings remain the same.

The ac supply shown in Figure 6 is replaced with a square-wave generator operating between $0$ and $+15\text{ V}$.

Figure 8 shows the trace of the new waveform displayed on the oscilloscope.

The time-base is set to $5.0\times {10}^{-4}{\text{ s div}}^{-1}$.

Figure 8

Calculate the frequency of the square waves.

frequency = .................... Hz

Figure 9 shows the arrangement with the square-wave generator connected to an RC circuit.

A capacitor C is placed in series with the resistor R.

The oscilloscope is connected across the capacitor C.

Figure 9

The capacitor charges and discharges.

Figure 10 shows the trace of the waveform displayed on the oscilloscope.

The settings of the oscilloscope remain the same as in part (d).

Figure 10

Deduce the time constant for the RC circuit, explaining each step of your method.

time constant = .................... s

State and explain a change to one control setting on the oscilloscope that would reduce the uncertainty in the value of the time constant.