AQA A Level Physics Paper 2 June 2025 question paper 7408/2

Information about the radius of a nucleus can be deduced from the closest approach of alpha particles and from electron diffraction.

Alpha particles, each with a kinetic energy of 5.59 MeV, are fired at a thin foil made of

Some of the alpha particles are scattered through an angle of 180°.

Estimate the radius of a 197 79Au nucleus from this information.

Explain why your answer to Question 01.1 is an estimate.

Electron diffraction gives a more precise value for the radius of the nucleus.

Sketch, on Figure 1, a graph of intensity against angle for electron diffraction by a nucleus. Go on to state the feature of this graph that is used to determine the radius of the nucleus.

Results from electron-diffraction experiments lead to the equation:

Show that the equation provides evidence for the constant density of nuclear material.

One of these assumptions is that particle motion is random.

State what is meant by random particle motion.

State two other assumptions required for this derivation.

When the temperature of a fixed mass of an ideal gas increases at constant pressure, the gas must expand.

Explain this expansion using the kinetic theory model.

Helium behaves as an ideal gas. The temperature of a sample of helium gas is increased from 27 °C to 77 °C.

Calculate the change in the average kinetic energy of a helium atom in the sample.

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

When water vapour is heated at constant volume, its specific heat capacity

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

mass of a water molecule = 3.0 × 10⁻²⁶ kg

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 × 10₂₄ atoms of plutonium-238 238Pu 94 .

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

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 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 × 10⁻¹⁰ s⁻¹ energy of alpha particle emitted by plutonium-238 = 8.94 × 10⁻¹³ J

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 °C. The ice does not form a liquid.

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

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

The laser heats the ice from an initial temperature of −25 °C to a temperature of 0.0 °C. The laser then transfers energy to vaporise the ice at 0.0 °C.

Determine whether the laser is able to vaporise 1.0 g of the ice that is initially at −25 °C before the battery needs to be recharged.

specific heat capacity of ice = 2.1 kJ kg⁻¹ K⁻¹ specific latent heat of fusion of ice = 334 kJ kg⁻¹ specific latent heat of vaporisation = 2500 kJ kg⁻¹

Mimas and Enceladus are moons of Saturn.

Mimas orbits at a height of 1.28 × 10⁸ m above the surface of Saturn. The orbital period of Mimas is 0.94 Earth days.

Enceladus orbits at a height of 1.80 × 10⁸ m above the surface of Saturn.

Calculate, in Earth days, the orbital period of Enceladus.

Titan is the largest moon of Saturn.

Figure 2 shows the variation of gravitational potential with distance from the centre of Saturn in the direction of Titan.

The dashed line shows the gravitational potential due to the mass of Saturn alone.

The solid line shows the total gravitational potential due to Saturn and Titan. The solid line ends at the surface of Titan.

A student suggests that, over the range of distances shown in Figure 2, the gravitational field strength due to the mass of Saturn alone is approximately constant.

Explain why the suggestion is correct.

At a point P, the resultant gravitational field strength due to Saturn and Titan is zero.

Determine, using the solid line in Figure 2, the distance from Saturn to P.

The centre of Titan is 12.22 × 10⁸ m from the centre of Saturn.

Show that the gravitational potential due to the mass of Titan at a distance of 12.08 × 10⁸ m from Saturn is about −7 × 10⁵ J kg⁻¹. Go on to determine the mass of Titan.

A material used between the plates of a capacitor has a dielectric constant of 7.0

State what is meant by a dielectric constant of 7.0

Figure 3 shows a circuit that is used to charge and discharge a capacitor.

The battery has negligible internal resistance.

The two resistors in the circuit are identical.

The capacitor is fully charged and the switch is then moved from position A to position B at time t = 0

Figure 4 shows the variation of the microammeter reading with t until t = 120 s.

The time constant of the discharging circuit is T.

Determine T using Figure 4.

Electronic engineers consider a capacitor to be fully discharged when t = 5 T.

The capacitor is fully discharged and then the switch is moved from position B to position A as shown in Figure 3.

Draw, on Figure 5, the variation of the microammeter reading with time after the switch is moved to position A. In Figure 5, the time is 0 at the instant when the switch is moved to position A.

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.

An ion travels in a circular path at a speed of 74.2 km s⁻¹ and at a distance of 4.22 × 10⁸ 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.

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 × 10⁻¹⁹ C and a mass of 5.31 × 10⁻²⁶ kg.

The ion moves with a speed of 74.2 km s⁻¹ in a circle of radius 4.22 × 10⁸ 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.

The plasma torus contains two ions X and Y as shown in Figure 8. X has a charge of +2 e. Y has a charge of +1 e. Assume that each ion acts as a point charge.

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

An object on the surface of a moon has an escape velocity v. The moon has a density ρ and radius R. Another moon X has a density 2ρ and radius .

What is the escape velocity for an object on the surface of X ?

In an investigation of Boyle’s law, a sealed syringe of cross-sectional area 1.0 × 10⁻⁴ m² contains 12 cm³ of gas. The gas is initially at atmospheric pressure.

A weight of 2.5 N is then suspended from the plunger of the syringe as shown in the diagram.

The temperature of the gas in the syringe and the atmospheric pressure are constant.

What is the new volume of gas in the syringe?

The graph shows the variation of pressure with volume for a constant mass of a gas.

The temperature of the gas:

The graph shows how the pressure of a fixed mass of gas varies with temperature. The gas has a constant volume.

Which expression gives a value for absolute zero in °C ?

Two charged metal spheres have charges + Q and − q. The magnitude of + Q is greater than the magnitude of − q.

In which diagram are the electric field lines correct?

Two metal spheres each have radius r and charge Q. The force between them is F when the distance between their centres is x. Two other metal spheres each have radius and charge 2Q.

What is the force between these two spheres when the distance between their centres is x ?

A particle has mass m and charge q.

The particle is moved a distance d through a potential difference V.

What is the change in electric potential energy?

The diagram shows an electron in an electric field represented by equipotentials.

Which arrow shows the direction of the electric force on the electron?

The diagram shows point charges Q and q.

Q and q have charges of opposite sign.

The magnitude of the charge of Q is greater than the magnitude of the charge of q.

The electric field strength is zero at one of the points A, B, C or D.

At which point is the electric field strength zero?

The diagram shows two parallel conducting plates at potentials of −20 V and −10 V.

The displacement x is measured from the bottom (−20 V) plate.

Which graph shows how the electric field strength E varies with x ?

A parallel-plate capacitor X with the plates separated by air has a capacitance of 100 μF.

Another parallel-plate capacitor Y has plates that are double the height of the plates of X.

The plates of Y have the same separation and the same width as the plates of X. The space between the plates of Y is filled with a material of dielectric constant 3.0

What is the capacitance of Y ?

A capacitor is initially uncharged and is then charged using a constant current. This is achieved by reducing the resistance of a variable resistor R as the charge on the capacitor increases.

The capacitor has a capacitance of 300 mF and is fully charged in a time t = 100 s. The cell has an emf of 2.0 V and negligible internal resistance. The charging current is 6.0 mA.

What is the resistance of R at t = 30 s ?

Four identical magnets slide down four ramps P, Q, R and S of the same length and width. The slope of each ramp is the same.

The table shows the resistivity and thickness of each ramp.

Friction is the same for each ramp. The time t for each magnet to slide down the entire length of its ramp is measured.

Which row shows the ramp with the smallest t and the ramp with the largest t ?

A horizontal wire is perpendicular to a horizontal uniform magnetic field of flux density B. The wire has length L and diameter d. The current in the wire is I.

The magnetic force acting on the wire is equal in magnitude and opposite in direction to the weight of the wire so that the wire is supported.

The wire is replaced with a second wire in the same orientation and position. The second wire is made of the same material and has length and diameter 2d.

What current is required to support the second wire?

A coil rotates at a constant angular speed in a uniform horizontal magnetic field. The diagram shows the instant when the plane of the coil is horizontal.

cross-sectional area of coil = 20 × 10⁻³ m² number of turns in coil = 500 turns magnetic flux density = 50 mT frequency of rotation = 50 Hz

What is the mean induced emf, in V, as the coil rotates through π rad from the position

A metal block has dimensions 30.0 cm × 10.0 cm × 5.0 cm as shown.

The block is moved at a constant horizontal velocity of 5.0 cm s⁻¹ through a uniform vertical magnetic field so that an emf is induced across the block.

The magnetic field has a magnetic flux density of 2.5 mT.

What is the induced emf?

A transformer is used to connect an ac power supply to a 100 W filament lamp.

When the lamp is operating at its rated power, the power supply has a peak potential difference of 50 V and supplies a peak current of 5.0 A.

What is the efficiency of the transformer?

The diagram shows an ac signal displayed on an oscilloscope screen.

The time base is set to 5 μs div⁻¹.

What is the frequency of the signal?

A radiation meter is placed at a distance d from a source of gamma radiation. The corrected count rate is 800 counts per second.

When the radiation meter is moved a further 10 cm from the source the corrected count rate is 600 counts per second.

What is d ?

241Am decays to one of two excited states of 237 Np by emitting an alpha particle. 95 93 The excited 237 93 Np nucleus then decays with the emission of a gamma photon.

What is the energy of the emitted gamma photon that has the shortest wavelength?

Which decay produces an atom with electrons in excited states?

Polonium-210 decays into lead-206 by emitting an alpha particle.

mass of nucleus of polonium-210 = 209.983 u mass of nucleus of lead-206 = 205.975 u mass of alpha particle = 4.003 u

Assume that the recoil speed of the lead nucleus is negligible.

What is the kinetic energy of the emitted alpha particle?

Which is not a use of water in the nuclear industry?

The purpose of a moderator in a thermal nuclear reactor is to:

The plot of average binding energy per nucleon is shown. P, Q and R indicate regions of the plot.

In which region or regions labelled on the plot do nuclei undergo fission to release energy?