AQA A Level Physics Paper 2 November 2020 question paper 7408/2

A perfectly insulated flask contains a sample of metal M at a temperature of –10 °C.

Figure 1 shows how the temperature of the sample changes when energy is transferred to it at a constant rate of 35 W.

State the melting temperature of M.

Explain how the energy transferred to the sample changes the arrangement of the atoms during the time interval t_A to t_B.

State what happens to the potential energy of the atoms and to the kinetic energy of the atoms during the time interval t_A to t_B.

Describe how the motion of the atoms changes during the time interval t_B to t_C.

The sample has a mass of 0.25 kg.

Determine the specific heat capacity of M when in the liquid state. State an appropriate SI unit for your answer.

Table 1 shows the specific latent heats of fusion l for elements that are liquid at similar temperatures to M.

M is known to be one of the elements in Table 1.

Identify M.

Figure 2 shows a moon of mass m in a circular orbit of radius r around a planet of mass M, where m << M.

The moon has an orbital period T. T is related to r by

where k is a constant for this planet.

Table 2 gives data for two of the moons of the planet Uranus.

Calculate the orbital radius X of Umbriel.

Calculate the mass of Uranus.

Table 3 gives data for three more moons of Uranus.

Deduce which moon in Table 3 has the greatest escape velocity for an object on its surface. Assume the effect of Uranus is negligible.

A spring mechanism can project an object vertically to a maximum height of 1.0 m from the surface of the Earth.

Determine whether the same mechanism could project the same object vertically to a maximum height greater than 100 m when placed on the surface of Ariel.

Mass spectrometers are used to measure the masses of ions.

Figure 3 shows one part of a mass spectrometer.

A narrow beam consists of positive lithium ions travelling at different speeds. The beam enters a region where there is an electric field and a magnetic field. The directions of the uniform electric field of strength E and the uniform magnetic field of flux density B are shown on Figure 3.

Most ions are deflected from their original path. Lithium ions that travel at one particular speed are not deflected, and pass through the small aperture.

The positive lithium ion A in Figure 3 moves at a speed v.

Draw two labelled arrows on Figure 3 to show the directions of the electric force F_E and the magnetic force F_M acting on A.

Lithium ions travelling at 1.5 × 10⁵ m s⁻¹ pass through the small aperture.

Calculate E.

B = 0.12 T

Ions that pass through the small aperture enter a second uniform magnetic field of flux density B. Ions of different mass are separated because they follow different paths as shown in Figure 4.

Ions of mass m and charge q travelling at speed v follow a circular path in the uniform magnetic field.

Show that the radius r of the circular path is given by

The ions of different mass are deflected and strike the detector surface at different distances from the small aperture as shown in Figure 4.

A singly-charged lithium ion (⁶₃Li⁺) passes through the small aperture.

Calculate the distance between the small aperture and the point where this ion strikes the detector surface.

B = 0.12 T

Figure 5 shows a different type of mass spectrometer working with lithium ions.

A stationary⁷₃Li⁺ ion in the lithium sample is at the mid-point between the parallel electrodes. The⁷₃Li⁺ ion accelerates towards aperture P.

Determine the speed of the ion when it emerges through aperture P.

⁶Li⁺ Li⁷⁺ L ₃ and₃ ions are produced in the sample simultaneously and travel a distance from aperture P to the detector. For each type of ion, the time interval between production and detection is measured.

Discuss how the masses of the ions can be deduced from the measurement of these time intervals.

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 V.

Calculate the rms voltage of the supply.

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

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

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 V.

Figure 8 shows the trace of the new waveform displayed on the oscilloscope. The time-base is set to 5.0 × 10⁻⁴ s div⁻¹.

Calculate the frequency of the square waves.

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.

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 Question 04.4.

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

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

Figure 11 shows alpha particles all travelling in the same direction at the same speed. The alpha particles are scattered by a gold (¹⁹⁷₇₉Au) nucleus. The path of alpha particle 1 is shown.

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 4 comes to rest at a distance of 5.5 × 10⁻¹⁴ m from the centre of the

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 × 10⁻²⁷ kg

The nuclear radius of¹⁹⁷₇₉Au is 6.98 × 10⁻¹⁵ m.

Calculate the nuclear radius of¹⁰⁷₄₇Ag.

All nuclei have approximately the same density.

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

A thermal nuclear reactor uses enriched uranium as its fuel. This is fuel in which the ratio of U-235 to U-238 has been artificially increased from that found in naturally-occurring ore.

Describe what happens when neutrons interact with U-235 and U-238 nuclei in a thermal nuclear reactor.

The amounts of U-235 and U-238 in the ore decrease due to radioactive decay at different rates.

A sample of uranium ore today contains 993 g of U-238 The mass of U-238 in this sample was greater 2.00 × 10⁹ years ago.

Show that the mass of U-238 in this sample at that time was about 1.4 kg.

decay constant of U-238 = 1.54 × 10⁻¹⁰ year⁻¹

A thermal nuclear reactor requires a minimum of 3.0% of its uranium mass to be U-235

The ratio of U-235 to U-238 in the ore has changed over time. 2.00 × 10⁹ years ago, the sample in Question 06.2 contained 52 g of U-235

Deduce whether the sample had a high enough U-235 content to be used in a reactor

When an ideal gas at a temperature of 27 °C is suddenly compressed to one quarter of its volume, the pressure increases by a factor of 7

What is the new temperature of the gas?

The diagram shows two flasks X and Y connected by a thin tube of negligible volume.

The flasks contain an ideal gas.

The volume of X is twice the volume of Y. When X is at a temperature of 100 K and Y is at a temperature of 400 K there is no net transfer of particles between the flasks.

X contains gas of mass m.

What is the mass of gas in Y ?

A sample P of an ideal gas contains 1 mol at an absolute temperature T. A second sample Q of an ideal gas contains mol at an absolute temperature 2T.

The total molecular kinetic energy of P is E.

What is the total molecular kinetic energy of Q ?

An ideal gas is contained in a cubical box of side length a. The gas has N molecules each of mass m.

What is the pressure exerted by the gas on the walls of the box?

Which statement is true about an experiment where Brownian motion is demonstrated using smoke particles in air?

The graph shows how the gravitational potential V varies with the vertical distance d from the surface of the Earth.

What does the gradient of the graph represent at the surface of the Earth?

What is the angular speed of a satellite in a geostationary orbit around the Earth?

Two fixed charges of magnitude + Q and +3 Q repel each other with a force F. An additional charge of −2 Q is given to each charge.

What are the magnitude and the direction of the force between the charges?

At a distance L from a fixed point charge, the electric field strength is E and the electric potential is V.

What are the electric field strength and the electric potential at a distance 3 L from the

Which diagram shows lines of equipotential in steps of equal potential difference near an isolated point charge?

A positive charge of 2.0 × 10⁻⁴ C is placed in an electric field at a point where the potential is +500 V.

What is the potential energy of the system?

Two charges P and Q are 100 mm apart. X is a point on the line between P and Q where the electric potential is 0 V.

What is the distance from P to X ?

An uncharged capacitor is connected to a power supply which supplies a constant current of 10 μA.

After 100 ms, the potential difference across the capacitor is 5.0 kV.

What is the capacitance of the capacitor?

When a parallel-plate capacitor is connected across a battery, the energy stored in the capacitor is W.

The battery remains connected as the distance between the capacitor plates is halved.

What is the energy now stored in the capacitor?

A parallel-plate capacitor is made using a sheet of dielectric material between, and in contact with, two plates. The properties of four sheets of dielectric material are shown.

Which sheet will produce the maximum capacitance?

A 10 μF capacitor stores 4.5 mJ of energy. It then discharges through a 25 Ω resistor.

What is the maximum current during the discharge of the capacitor?

The diagram shows a current I in a vertical square coil. The coil can rotate about an axis OO’. The plane of the coil is at right angles to a uniform horizontal magnetic field of flux density B.

Which statement is correct?

The diagram shows a small rectangular coil falling between two magnetic poles.

The coil is shown at four instants as it passes through the magnetic field.

At which instant will the induced emf be a maximum?

An alternating emf is induced in a coil rotating in a magnetic field.

What is the phase difference between the magnetic flux linkage through the coil and the

The diagram shows the variation with time t of the magnetic flux density B of the field linking a coil.

Which graph shows the variation of induced emf ε in the coil during this time interval?

A coil P is connected to a cell and a switch. A closed coil Q is parallel to P and is arranged on the same axis.

Which describes the force acting on Q after the switch is closed?

A point source emits gamma radiation. The intensity I of the radiation is measured at different distances d from the source.

Which graph will show a straight line through the origin?

The number of parent nuclei in a sample of a radioactive element is N at time t. The radioactive element has a half-life The rate of decay is proportional to

The table shows the masses of three particles.

What is the mass difference of a⁷₃Li nucleus?

The mass of the fuel in a fission reactor decreases at a rate of 6.0 × 10⁻⁶ kg hour⁻¹.

What is the maximum possible power output of the reactor?