5.4 Nuclear Decay

Definition of fission

State what is meant by fission (1)

📚 Oct 2022

• A massive nucleus splits into two (or more) smaller nuclei/fragments (of roughly equal mass and some neutrons)

State what is meant by nuclear fission (1)

📚 Jun 2021

• A massive/large nucleus splits into smaller fragments

Application of radioactive substances

The isotope 32P is injected into a person and collects in the tumour. Radiation is detected outside the person’s body. 32P is a positron emitter with a half-life of almost fifteen days. Explain why 32P is suitable for this procedure (4)

📚 Oct 2022

• Positrons annihilate with electrons to produce gamma radiation
• Gamma radiation can penetrate the body
• Half life is long enough to allow the procedure to be performed
• Half life is short enough to avoid unnecessarily large radiation dose

Cloud chamber, bubble chamber tracks

A student makes the following observations: the alpha particle tracks are thick and straight; the beta particle tracks are thin and twisted. Explain these observations (4)

📚 Jun 2023

• The thickness of the track related to the ionising ability of the particle (not its mass)
• Alpha is strongly ionising and beta is only moderately ionising (so alpha tracks are thick and beta tracks are thin) [Allow a comparison of ionising power of alpha with that of beta]
• The shape of the track related to the mass of the particle (not its ionising ability)
• Alpha particles are massive particles and beta particles are not massive particles (so alpha tracks are straight and beta tracks are twisted) [Allow a comparison of alpha mass with beta mass]

Binding energy per nucleus vs stability

The binding energy per nucleon of helium is relatively large. Explain why this makes the helium nucleus particularly stable (2)

📚 Jan 2024

• The binding energy per nucleon is the energy required to remove a nucleon from the nucleus
• Large energy is required to break the helium nucleus apart
• Decay products (of helium) have a lower binding energy per nucleon

Conservation of momentum

Explain why not all of the energy from the decay is released as kinetic energy of the alpha particle (2)

📚 Jun 2022

• Momentum must be conserved (in the decay)
• The lead nucleus must recoil after the decay Or the lead nucleus moves in the opposite direction to the alpha particle

Explain why the emission of an antineutrino in the decay leads to a range of energies for the beta- particles (2)

📚 Oct 2022

• Momentum is conserved (so the Ba nucleus recoils)
• Energy released is shared (randomly) between the β− and ν̅ Or the energy is shared between the 3 particles in the decay

Explain why the alpha particle must have an energy greater than the minimum energy for the reaction to take place (2)

📚 Oct 2023

• Momentum (and energy) is conserved
• (So) products must have \(E_{\text{k}}\) / momentum after the reaction (as the alpha particle has momentum before the reaction)

Explain why the kinetic energy given to the alpha particle is just less than 5.9 MeV (4)

📚 Jan 2022

• Use of 1 u = 934 MeV (ecf from (b) [Accept calculation from first principles]
• The mass of the Fr nucleus is much greater than the mass of the α
• Momentum is conserved so (recoil) velocity of Fr nucleus is much less than the velocity of the α
• So the kinetic energy of the α is much greater than the kinetic energy of the Fr Or (after the decay) the α has most of the kinetic energy

Suggest why the majority of the energy released is shared between the beta particle and the antineurino (1)

📚 Oct 2021

• The mass of the Ni nucleus is much larger than total mass of the other two particles

Explain why there is a range of energies for the beta particles emitted in the decay of a sample of potassium-40 (2)

📚 Jan 2021

• Momentum/KE is given to 3 particles in the decay Or (KE of Ca is negligible so) KE for the beta-neutrino pair was constant
• The energy split between the beta particle and the neutrino is random Or the momentum of the emitted beta particle varies Or The (anti) neutrino energy varies

Energy released during fission / fusion

Explain why energy is released when a nucleus undergoes fission (2)

📚 Jan 2024

• A large nucleus splits (into two nuclei plus neutrons)
• The binding energy increases, (so energy is released) [Accept binding energy per nucleon increases] Or There is a decrease in (total) mass, (so energy is released)

Explain why energy is released when hydrogen nuclei fuse to form helium nuclei (2)

📚 Jun 2023

• In the fusion process mass decreases
• So energy is released according to \(∆E = c^{2}∆m\) Or energy is released to conserve mass-energy Or binding energy per nucleon increases

Range of alpha / beta / gamma radiation

State why alpha radiation will not affect the recorded count rate (1)

📚 Jun 2024

• The alpha radiation will not penetrate the lead
• Or The lead will absorb the alpha radiation

Explain which type of radiation is emitted from the source. You should refer to the penetration of each type of radiation through each sheet of absorber (4)

📚 Jan 2024

• Alpha radiation would not pass through the sheet of paper
• No change in count rate when paper placed (between source and GM tube), so there can’t be any alpha radiation
• There can’t be any gamma radiation, as gamma radiation would pass through the aluminium sheet Or There can’t be any gamma radiation, as count rate decreases to background with aluminium sheet.
• It must be beta radiation as beta radiation would not pass through the aluminium sheet.

*Ultraviolet radiation is produced when alpha particles interact with air. This can be used to detect alpha particles when a nuclear reactor is decommissioned. Explain how UV is produced by alpha particles in the air, and why detecting UV has advantages compared with detecting alpha particles directly (6)

📚 Jun 2021

• IC1 Energy from the α particles is transferred to atoms/molecules in the air
• IC2 An electron in the atom/molecule is promoted to a higher energy state Or the atom/molecule/electron is excited
• IC3 When the electron return to a lower energy state a photon (of uv- radiation) is emitted Or when the atom/molecule/electron de-excites, a photon (of uv-radiation) is emitted
• IC4 α radiation is strongly ionising and so has a short range (in air)
• IC5 Ultraviolet radiation is weakly ionising (and has long range in air)
• IC6 UV-radiation can be detected much further from the source so is safer

Core practical: measuring radioactivity

Explain one modification to her method that would give a more accurate value for the count rate (2)

📚 Jun 2024

• EITHER
• Determine the background count (rate)
• Subtract background count (rate) from the recorded count (rate) to eliminate systematic error Or Subtract background count from the recorded count to prevent the count rate being overestimated
• OR
• Record the count for a longer time interval Or Record the count more than once and calculate a mean value
• This will reduce the effect of random variation on the count rate Or this will decrease the percentage uncertainty

Practical: Investigate the absorption of radiation by lead

Explain a precaution necessary when handling a sample of an alpha emitting isotope (2)

📚 Jun 2020

• Handle the source with tongs
• As alpha particles can only travel a few cm in air [Accept alpha particles have a very short range] Or The greater the distance, the lower the intensity of radiation received
• OR
• Handle the source for as short a time a possible
• As the ionising effect is cumulative

5.3 Thermodynamics

The kinetic model

Explain why the pressure of the air inside the scuba tank increases as the temperature increases. Your answer should refer to the motion of the air molecules (6)

📚 Jan 2023

• IC1 As the temperature increases the (average) kinetic energy of the (air) molecules increases
• IC2 So mean/average speed of the air molecules increases
• IC3 The (average/mean) change of momentum of air molecules when colliding with the tank/walls increases
• IC4 The rate of collision of air molecules with the tank/walls increases
• IC5 The rate of change of momentum increases and so the force on the tank/walls, increases
• IC6 The pressure (exerted by the gas) increases, since p = F/A

The pressure of the trapped air increases when the air is forced into a smaller volume. Explain why, using ideas of molecular motion (4)

📚 Jun 2021

• The atoms/molecules make more frequent collisions with the glass tube Or The atoms/molecules have a higher rate of collision with the glass tube Or The atoms/molecules make more collisions per second with the glass tube (Do not accept collisions between molecules)
• The rate of change of momentum of the atoms/molecules increases
• The force exerted on the glass tube increases
• (Pressure exerted by the gas increases) as pressure is force per unit area

*The pressure inside a football decreases as the temperature of the air inside falls. The volume of the ball remains constant. Explain why, in terms of the motion of the molecules (6)

📚 Jun 2020

• As the temperature of the air decreases the average/mean kinetic energy of the molecules decreases
• So the (root mean square) velocity/speed of the molecules decreases Or (Since Ek = p^2/2m) the (average) momentum of the molecules decreases
• The change of momentum of a molecule during a collision with the container walls decreases
• The rate of collision of molecules with the walls of the container decreases
• So the rate of change of momentum decreases and so the force on the container walls decreases
• Hence the pressure exerted by the gas decreases, since p = F/A

Melting

*Describe how the internal energy of the wax changes as the wax cools. You should refer to the energy of the wax molecules as the liquid wax cools and becomes solid, and the solid wax cools (6)

📚 Jun 2023

• IC1 The internal energy of the wax decreases during cooling Or The internal energy of the wax decreases as time passes
• IC2 The internal energy of the wax is the sum of potential energy and kinetic energy of the molecules
• IC3 As the temperature of the wax decreases, the (molecular) kinetic energy
• decreases
• IC4 Between times X and Y the (liquid wax is solidifying and the molecular) potential energy decreases
• IC5 Between times X and Y the temperature is constant and so there is no change in (molecular) kinetic energy
• IC6 At time Y the wax has solidified

Boiling

Explain why the liquid nitrogen boiled when the banana as submerged in the liquid nitrogen (2)

📚 Jan 2024

• Energy is transferred from banana to liquid nitrogen
• The molecular potential energy of nitrogen molecules increases (as the nitrogen boils) Or This provides the latent heat of vaporisation (of the nitrogen) Or This provides the latent heat to change state (of the nitrogen)

Core practical: determining specific heat capacity

A heater is used to increase the temperature of the water. State why the amount of energy supplied by the heater will be different from the value of delta R calculated in (a) (1)

📚 Jan 2023

• Energy is transferred (from the water) to the surroundings Or Not all of the energy from the heater is used to raise the water temperature

Core practical: calibration of thermistor

*A student is planning an experiment to investigate how the resistance of a thermistor changes with temperature. The student wants to use the temperature range 0dC to 100dC. Describe a method the student could use to determine values of resistance and temperature over this range. You should include one precaution the student should take to ensure accurate measurements. You do not need to draw a circuit diagram. (6)

📚 Oct 2023

• IC1 Connect the thermistor to a suitable circuit with voltmeter and ammeter Or Connect the thermistor to an ohmmeter
• IC2 Place the thermistor in a water bath Or place the thermistor in a beaker of water
• IC3 Add ice to reduce the water temperature to \(0^{o}C\)
• IC4 Heat the water and use a thermometer to measure the temperature Or Heat the water and use a temperature sensor and datalogger to measure the temperature
• IC5 Determine the resistance R (for each temperature) using R = V/I Or Measure the resistance (for each temperature) by reading from ohmmeter
• IC6 Stir the water (to ensure that the thermistor is at the temperature measured by the thermometer)
• Or Place the thermometer near to the thermistor (to ensure that the thermistor is at the temperature measured by the thermometer)
• Or Stop heating and wait before taking readings
• (to prevent it heating the thermistor)
• Or Switch current off between readings
• Or Read thermometer at eye level

Resonance

A website suggests that water molecules absorb energy because the microwaves produced by the oven cause the water molecules to resonate. Comment on this suggestion (2)

📚 Jun 2020

• The natural frequency of the water molecule is about 10 GHz
• The microwave radiation frequency (2.45 GHz) is not at/about the natural frequency of the water molecule and so this is not resonance
• Or
• The driving frequency is not is not at/about the natural frequency of the water molecule and so this is not resonance

States of matter

Suggest why the transfer of energy from the microwaves may be less efficient for ice than for liquid water (2)

📚 Jun 2020

• Ice is a solid and so the molecules have fixed positions
• This prevents the molecules in the solid ice from rotating Or only molecules in liquid water around the ice can rotate

5.5 Oscillations

Maximum acceleration of particles in a container

Suggest why the particles of paint in the can will experience a maximum acceleration that is different from the answer to (ii) (1)

📚 Oct 2022

• The particles are free to move inside the can
• Or Not all the particles will move with simple harmonic motion
• Or Amplitude/frequency/period of oscillation of particles is different to amplitude of can
• Or The particles may continue to move upwards as the can starts moving downwards
• Or The particles may collide with each other
• Or the force on the paint particles is not equal to the force on the can.

Energy Conservation

The teacher turns the tube upside down, and the lead shot falls through a distance d. The teacher repeats this N times and measures the final temperature of the lead shot. The change in temperature delta theta off the lead shot is calculated. The teacher uses d, N, delta theta to determine a val for the s.h.c. of the lead. Access whether this method would produce an accurate value for c (2)

📚 Jun 2022

• Not all the energy will be used to increase the temperature of the lead shot Or some energy will be transferred to the surroundings Or not all the lead shot will fall through a distance d
• The method will not be accurate, as it will give a value of c that is too large Or The method will not be accurate as the (measured) temperature change will be too small

The student makes the following conclusion: “As the frequency is increased, the amplitude of the mass increases to a maximum, so energy conservation does not apply to this situation.” Explain whether her conclusion is correct (3)

📚 Jun 2023

• Some of the energy from the student’s hand is transferred to the oscillating mass and some of the energy is transferred to surroundings
• When the amplitude is a maximum, minimum energy is transferred to surroundings [Accept “at the natural frequency” or “resonance” for when the amplitude is a maximum]
• (In a closed system) total energy is constant so the student is incorrect.

Damping

Explain how damping reduces the large amplitude of vibration of the car on its suspension (2)

📚 Jan 2023

• (Kinetic) energy is transferred from the car Or (Kinetic energy transferred to the suspension/dampers)
• The energy is dissipated to the surroundings [so the vibration energy decreases]

Explain why the maximum velocity of the oscillating mass decreased over time (2)

📚 Oct 2023

• Energy is transferred out of the oscillating system Or energy is dissipated (to surroundings)
• Because work is done by/against resistive forces

When the building oscillates, the floor moves but the lead box tends to remain at rest. Suggest why the lead box tends to remain at rest (2)

📚 Jun 2024

• The motion of the box is (strongly) damped
• Amplitude at resonance is small
• Lead box has a large mass/inertia
• A large force is needed to set box into motion

When the wind blows at a certain speed, the building oscillates with a frequency of 0.17 Hz Explain why the damper system should be designed to oscillate at this frequency (2)

📚 Jun 2024

• Match the natural frequency (of the dampers) to the driving frequency
• So that there is an efficient / maximum transfer of energy (to the dampers)

As the floor moves, the rollers force oil through holes in the steel plate. Explain why this reduces the amplitude of oscillation of the building (2)

📚 Jun 2024

• Work is done (by roller) as oil is forced through the holes
• So energy is transferred from the building (and not returned) Or energy is transferred to the surroundings (and not returned) [Accept “dissipated” for “transferred to surroundings”]

The mass is submerged in water as shown. The mass is set into oscillation as before. Explain how the water would affect the amplitude of oscillation of the mass (3)

📚 Jun 2020

• There would be viscous/drag forces on the mass as it moved through the water
• This would remove energy (from the oscillation) Or this causes damping
• The amplitude would decrease over time

Resonance

* A teacher is teaching her class about the phenomenon of resonance. To do this, she uses a drinking glass to produce sound in two different ways. When the glass is gently struck, the glass emits sound for a short time. When a wet finger is slid around the top of the glass, it is possible to produce a loud continuous sound. Explain these observations (6)

📚 Jun 2022

• IC1 Striking the glass sets the glass into (free) oscillation.
• Or the oscillation is damped and the amplitude (of oscillation) decreases (quickly to zero).
• IC3 Sliding a wet finger around the top of the glass drives/forces the glass/system into oscillation.
• IC4 The driving frequency (produced by the wet finger) is equal/close to the natural frequency (of oscillation) of the glass/system
• IC5 Resonance occurs and there is an efficient/maximum transfer of energy
• IC6 The amplitude (of oscillation) increases (and transfers energy to the air)

Explain why unusually high tides are observed in the bay (3)

📚 Oct 2022

• Period of the tide matches natural period of oscillation of water in the bay [accept references to frequency]
• Efficient/maximum transfer of energy (into water in the bay) Or Resonance occurs
• Amplitude (of tide) increases Or There is a maximum amplitude

Explain why the amplitude of vibration increases at a particular speed (2)

📚 Jan 2023

• The car (body) is driven/forced into oscillation at its natural frequency Or The driving/forcing frequency is the same as the natural frequency of the car (body) Or the driving/forcing frequency from the road is the same as the natural frequency (of the car body)
• There is a maximum transfer of energy (to the car body)

The student increases the frequency at which she oscillates her hand. She keeps the amplitude of oscillation of her hand constant. She observes that the amplitude of the oscillation of the mass increases to a maximum and then decreases. Explain this observation. (3)

📚 2023 Jun

• When the driving frequency is equal to the natural frequency of the mass-spring system
• Resonance occurs
• There is a maximum transfer of energy (to the mass-spring system and the amplitude increases)

At a particular frequency, the loudspeaker cone starts to oscillate with a very large amplitude. Explain why this effect is observed (2)

📚 Jan 2022

• The driver frequency of the coil matches the natural frequency of the cone
• There is a maximum transfer of energy (from the coil to the cone)
• Resonance occurs

Explain what is meant by resonance (3)

📚 Jan 2021

• An oscillating system is driven/forced at its natural frequency
• There is a maximum transfer of energy
• Resulting in an increasing/maximum amplitude of oscillation

The bee’s wings oscillate at a frequency of 240 Hz, but the muscles only oscillate at a frequency of 60Hz. Suggest how impulses applied at 60Hz can maintain an oscillation at 240 Hz (2)

📚 Jan 2021

• The frequency of oscillation of the wings is a multiple of the muscle frequency
• Impulses are always applied at the same point in the cycle (of the wing's oscillation)
• So there will still be an efficient transfer of energy from the muscles to the wings

The microwave radiation causes the water molecules to rotate. Explain how this cooks the food (3)

📚 Jun 2020

• The (rotating) water molecules collide with other molecules (in the food)
• There is a transfer of kinetic energy to (adjacent) molecules (in the food)
• This increases the internal energy and hence the temperature of the food Or this increases the (average) kinetic energy (of the molecules) and hence the temperature of the food

Definition of simple harmonic motion

State what is meant by simple harmonic motion (2)

📚 2024 Jun

• There is a (resultant) acceleration / force that is proportional to the displacement from the equilibrium position
• and (always) acting towards the equilibrium position

Explain why the motion of the mass was simple harmonic motion (2)

📚 2023 Oct

• There is a (resultant) force that is proportional to the displacement from the equilibrium position
• and (always) acting towards the equilibrium position

State what is meant by simple harmonic motion (2)

📚 2023 Jun

• For an object to move with simple harmonic motion
• there must be an acceleration/(resultant) force that is proportional to the displacement from the equilibrium position
• and (always) acting towards the equilibrium position

State why the crib will oscillate with simple harmonic motion (2)

📚 Oct 2021

• (When the cradle is displaced): there is a (resultant) acceleration/force that is proportional to the displacement from the equilibrium position
• and (always) acting towards the equilibrium position
• (An equation with symbols defined correctly is a valid response for both marks)

Explain why the mass moves with simple harmonic motion (2)

📚 Jun 2021

• (The mass meets the conditions for simple harmonic motion as)
• There is a (resultant) force acting on the mass which is proportional to its displacement from its equilibrium position.
• The force is always directed towards the equilibrium position (An equation with symbols defined, and the negative sign justified, may be a valid response for both marks

State what is meant by simple harmonic motion (2)

📚 Jan 2021

• (For simple harmonic motion the) acceleration is:
• (directly) proportional to displacement from equilibrium position
• acceleration is in the opposite direction to displacement Or (always) acting towards the equilibrium position
• OR
• (For simple harmonic motion the resultant) force is:
• (directly) proportional to displacement from equilibrium position
• force is in the opposite direction to displacement Or (always) acting towards the equilibrium position

State the conditions for a mass to undergo simple harmonic motion (2)

📚 Jun 2020

• (For simple harmonic motion the) acceleration is:
• (directly) proportional to displacement from equilibrium position
• acceleration is in the opposite direction to displacement Or (always) acting towards the equilibrium position
• OR
• (For simple harmonic motion the resultant) force is:
• (directly) proportional to displacement from equilibrium position
• force is in the opposite direction to displacement Or (always) acting towards the equilibrium position
• (An equation with symbols defined correctly is a valid response for both marks

Forces on a simple harmonic oscillator

The maximum mass that the spring can support before being damaged is 25.0kg. Explain why the instructions state that the maximum mass is only 15.0 kg. (2)

📚 Oct 2021

• The maximum load the spring can support when oscillating is less than the maximum load the spring supports when in equilibrium.
• As when the mass is below the equilibrium position the FORCE EXERTED on the spring is GREATER than the force at equilibrium.

Inferences question

Suggest a disadvantage of basing the metre on the length of a ‘seconds pendulum’ (1)

📚 Jan 2021

• g varies depending upon location Or the metre would depend upon an accurate measurement of time Or the metre would depend upon the definition of the second

5.6 Astrophysics and Cosmology

Determination of stellar parallax

Describe how stellar parallax is used by astronomers (4)

📚 2023 Jan

• The star is viewed from two positions at 6 month intervals Or the star is viewed from opposite ends of the diameter of the Earth's orbit about the Sun
• The change in angular position of the star against backdrop of distant/fixed star is measured
• Trigonometry is used to calculate the distance to the star [Do not accept Pythagoras]
• The diameter/radius of the Earth’s orbit about the Sun must be known

Data inferences

Explain why hydrogen gas is no longer a large proportion of the gas in the Earth’s atmosphere. No further calculation is necessary. (2)

📚 2023 Jan

• There is a range of molecular speeds Or Some molecules will be travelling (much) faster than 1900 \(ms^{-1}\)
• So there will be some molecules with a speed greater than the escape velocity Or There will be some molecules with enough kinetic energy to escape

Astronomers think that there is a very large concentration of stars in the central region of the galaxy. Outside this central region the concentration of stars is very much less. All stars in the galaxy are rotating about its centre. It can be shown that the velocity v of a star a distance r from the centre of the galaxy is given by the expression \(v = \sqrt{\frac{GM}{r}}\). The graph shows how astronomers expect v to vary with r. Explain how the expression gives the variation of v with r shown in the graph (3)

📚 2022 Jan

• \(v \propto \sqrt{\frac{M}{r}}\)
• Within the central region M changes a lot (so v increases) Or Outside the central region M is approximately constant (so v decreases)
• As r increases v reaches a peak value as shown on the graph

When FRB sources were first discovered, some observers suggested that the bursts might be alien communications. Suggest why this is unlikely (2)

📚 Jun 2021

• Source luminosity is much larger than the luminosity of the Sun Or source is equivalent to the combined output of many Suns Or LFRB/LSun ~ 5 ×108
• Or the temperature would be much greater than that of the Sun (so not likely to be artificially produced)

H-R diagram

Explain how this H-R diagram shows that the star cluster is not a young star cluster. You should refer to groups of stars and their positions on this diagram (3)

📚 2023 Jun

• This cluster has red giant stars on the top right of the diagram
• And white dwarf stars bottom left of diagram
• A young cluster would only have a main sequence Or Red giant stars only occur in the later stages of a star’s evolution Or White dwarf stars only occur in the later stages of a star’s evolution

State where these stars would be located on a H-R diagram.

📚 Jun 2020

• At the top of the main sequence

Definition of main sequence star

State what is meant by a main sequence star (1)

📚 2023 Oct

• A main sequence star is a star that is fusing hydrogen in its core

State what is meant by a main sequence star (1)

📚 Oct 2021

• A main sequence star is fusing hydrogen (into helium) in the core of the star

Hubble’s law

In the 1950s, astronomers realised that they had made an error in their determination of distances to galaxies. Galaxies are twice as far away as astronomers had previously thought. Explain how this changed the age of the universe as calculated by astronomers (2)

📚 2022 Jun

• \(H_{\text{0}}\) is halved (for the same recessional velocity)
• So the (calculated) age of the universe doubles
• OR
• The universe would have taken twice as long to expand to its current size (assuming it expanded at the same rate)
• So the age of the universe is double what was previously thought

Access the validity of Hubble’s expression based on the data shown (3)

📚 2023 Oct

• EITHER
• A straight line through the origin would be consistent with Hubble’s expression
• There is scatter about the line but the points are distributed evenly
• So the expression may be valid (dependent upon MP2)
• OR
• A straight line through the origin would be consistent with Hubble’s expression
• (But) there are OUTLIERS and these are far from the line Or (But) only some of the points are close to the line
• So the expression may not be valid (dependent upon MP2)
• OR
• The gradient of the line is equal to \(H_{\text{0}}\)
• There is scatter about the line, so the value of \(H_{\text{0}}\) is uncertain
• So the expression may not be valid (dependent upon MP2)

Explain how a knowledge of the distances to distant galaxies has enabled astronomers to determine a value for the age of the universe (4)

📚 Oct 2021

• EITHER
• Distant galaxies are receding
• The velocity of recession can be calculated from the redshift
• A graph of recessional velocity against distance has a gradient equal to the Hubble constant \(H_\text{0}\)
• The age of the universe is \(\frac{1}{H\text{0}}\)
• OR
• Distant galaxies are receding
• The redshift can be calculated
• A graph of redshift against distance has a gradient equal to \(\frac{H_\text{0}}{c}\)
• The age of the universe is \(\frac{1}{H\text{0}}\)

Red shift

The recently launched James Webb Space Telescope is designed to operate in the infrared region of the spectrum. Explain why this will be helpful for studying very distant galaxies (2)

📚 2022 Oct

• Very distant galaxies have (very) large red shifts
• So their light has become infrared when it arrives (at the telescope)

State how astronomers knew that galaxies were moving away from the Earth. (1)

📚 2023 Oct

• The light / radiation (received) from the galaxies is red-shifted Or Wavelength of light / radiation (received) from the galaxies was longer than expected

Explain why there is a variation in the wavelength of the light from different points on the Sun (2)

📚 Oct 2021

• Light from the edge of the Sun moving toward the Earth is received with a shorter wavelength [Accept “point A” for “edge moving toward the Earth” and “blue shift” for “shorter wavelength”]
• Light from the edge of the Sun moving away from the Earth is received with a longer wavelength [Accept “point B” for “edge moving away from the Earth” and “red shift” for “longer wavelength”]
• There is a variation in the relative velocity between the Earth and different points on the Sun’s surface [Can be awarded if A and B incorrectly linked to change in wavelength]

Explain what is meant by redshift (2)

📚 Jan 2021

• Redshift is the (fractional) increase in the wavelength received
• Due to the source of radiation moving away from the observer

A massive planet orbits the red dwarf star Gliese 876. The planet was discovered after wavelength shifts in spectral lines were seen in the light received from the star. Explain how a massive planet orbiting a star can cause a change in the wavelength of the light received from the star (3)

📚 Jun 2020

• The (massive) planet exerts a (large) gravitational force on the star.
• The velocity of the star relative to the Earth changes.
• (which causes a varying) Doppler shift

Conditions for fusion (in a star)

*Explain the conditions required to bring about and maintain fusion in a main sequence star (6)

📚 Jan 2024

• IC1 There must be a (very) high temperature (in the core)
• or \(E_{\text{k}}\)]
• IC3 So that nuclei/protons get close enough to fuse
• IC4 Because there is an electrostatic repulsion between nuclei/protons
• IC5 There must be a (very) high density
• IC6 To give a high collision rate to maintain fusion Or To give a high collision rate to maintain high temperature

To achieve fusion in the ITER, a hot plasma is used. The plasma must be - at an extremely high temperature; - have sufficient density for fusion. Explain why these two conditions must be met (4)

📚 Jun 2023

• Very high temperature so that the nuclei have sufficient kinetic energy
• Nuclei must overcome electrostatic repulsion/forces [Allow a reference to overcome repulsion/forces due to positively charged nuclei]
• So that the nuclei come close enough to fuse
• Sufficient density so that the collision rate (between nuclei) is high (enough)
• Sufficient collision rate to maintain the (very high) temperature

*Nuclear fusion in the core of a star is the source of the star’s poewr output. Explain the conditions required to bring about and maintain nuclear fusion in stars. (6)

📚 Oct 2021

• IC1 There is a very high temperature (in the core)
• IC2 (So) nuclei/protons have a high kinetic energy
• IC3 (Sufficient) to overcome electrostatic repulsion
• IC4 And allow nuclei/protons to get close enough to fuse
• IC5 Gravitational forces produce a very high density (in the core)
• IC6 (So) the collision rate is high enough to sustain fusion

Scientists have been working to achieve a practical nuclear fusion reactor for more than 70 years. So far, this has been with only limited success. Explain the difficulties involved with fusion as a viable source of power on Earth. You should include reference to the conditions necessary for fusion to occur (4)

📚 Jun 2020

• (Very) high temperatures are needed to give hydrogen/nuclei/protons enough kinetic energy to overcome the repulsive force (between charges).
• High densities are needed to enable a high enough collision rate (of nuclei to sustain the fusion reactions)
• If the material/plasma undergoing fusion (on Earth) were to touch the container the temperature would decrease and fusion would stop Or ff the material/plasma undergoing fusion (on Earth) were to touch the container then the container would melt (and containment cease)
• (On Earth) strong magnetic fields are required because there are containment problems for a material undergoing fusion.

Parallax angles

Explain why parallax measurements can only be used to determine the distances to a relatively small number of stars (2)

📚 Jun 2022

• Parallax angle decreases as distance from the Earth increases Or parallax is only suitable for (relatively) close stars
• As parallax angle is too small to measure for distant stars

Standard candles

*The average distance between galaxies is many times greater than the size of our galaxy. Astronomers use standard candles to determine the distances to other galaxies. Describe how astronomers determine the luminosity of a standard candle and can use this to determine the distance to a nearby galaxy (6)

📚 Oct 2022

• IC1 Use (stellar) parallax to determine distance to a nearby standard
• candle,
• IC2 Measure the intensity of radiation from the standard candle Or Measure λmax and use Wien’s law to determine the (surface) temperature of the standard candle
• IC3 Use inverse square law to calculate the luminosity of the standard candle Or Use the Hertzsprung-Russell diagram to determine the luminosity of the standard candle
• IC4 Locate standard candle (in nearby galaxy)
• IC5 Standard candle has a known luminosity
• IC6 Measure intensity of radiation from the standard candle and use inverse square law to calculate distance to nearby galaxy
• Alternative for IC1, IC2 and IC3:
• IC1 Identify/observe a (Cepheid) variable star
• IC2 Measure the period/frequency of intensity variation
• IC3 Use a known relationship between period and luminosity to calculate the luminosity of the star

Describe how standard candles can be used to determine the distance to nearby galaxies (3)

📚 Jan 2023

• Identify/locate standard candle (in nearby galaxy)
• Measure intensity of radiation from the standard candle
• Use inverse square law to calculate distance

Describe how standard candles can be used to determine the distance to galaxies (4)

📚 Jan 2024

• Standard candles are stellar objects with a known luminosity
• Locate a standard candle in the galaxy
• Measure the intensity of the standard candle (on Earth)
• Use the inverse square law to calculate the distance to the standard candle

Describe how measurements of this standard candle (V1) could demonstrate that the Andromeda Nebula is not a nearby star cluster (4)

📚 Jun 2023

• The luminosity of the standard candle is known
• Measure/determine intensity of radiation from V1 [standard candle] [do not accept ‘calculate’]
• Use inverse square law to calculate distance (to cluster)
• Distance is too large (for V1 to be in a nearby cluster) [Must have the idea of being too far away, rather than just being far away]

Describe how standard candles can be used to determine distances to stars (3)

📚 Jan 2022

• The intensity (of radiation from the candle) is measured
• The luminosity of the standard candle is known
• The inverse square law is used to determine the distance [Accept reference to I=L/4πd^2 with symbols defined]

Life cycle of a star

Describe a possible evolutionary path for stars originally in area P. For each stage in the path, you should refer to the type of star (3)

📚 Jan 2024

• Stars in area P are (massive) main sequence stars
• Stars in area P evolve into area S and stars in area S evolve into area Q [Allow P → S → Q, or arrows on diagram]
• Stars in area S are red giant stars and stars in area Q are white dwarf stars [accept red supergiant for red giant]

*Main sequence stars evolve into red giant stars. Red giant stars eventually become white dwarf stars. Explain this evolutionary sequence. You should refer to the fusion processes occurring in the star. (6)

📚 Jun 2024

• IC1 Hydrogen fusion occurs in the core of the (main sequence) star
• IC2 Hydrogen (in the core) runs out
• IC3 The rate of fusion decreases and the star contracts
• IC4 The temperature rises (in the core) and fusion of helium begins
• IC5 The star expands (and cools) to form a red giant star
• IC6 (Helium) fusion stops and the star collapses to a white dwarf star Or helium runs out and the star collapses to a white dwarf star

*The position of a star on the HR diagram changes as the star evolves. Explain how a star like the sun evolves as it progresses from zone Z3 to its final position on the HR diagram (6)

📚 Jan 2022

• IC1 The star is fusing hydrogen in its core
• IC2 When fusion ceases (the core of the star cools and) the core collapses/contracts (under gravitational forces)
• IC3 The star (moves to Z4 as it expands and) becomes a red giant star
• IC4 Temperature (in the core) is high enough for helium fusion to begin
• IC5 Helium begins to run out and then fusion ceases
• IC6 The star becomes a white dwarf (in Z2)

Fate of the universe

The ultimate fate of our universe is uncertain. Explain how the existence of dark matter contributes to this uncertainty (2)

📚 Jan 2023

• The ultimate fate of the universe depends upon the (average) density of the universe Or the (average) density of the universe must be compared with the critical density of the universe
• The amount of dark matter is uncertain (so the average density is uncertain)

The ultimate fate of the universe may be a closed universe, but astronomers cannot be sure what their current models predict. Explain why astronomers cannot be sure that the universe if closed (2)

📚 Jan 2022

• (For a closed universe) the density of the universe must be greater than the critical density
• And the (average) density of the universe is uncertain Or the amount of dark matter is uncertain

Dark matter

The observed variation of v with r has been added to produce the graph below. Suggest why the “observed” velocity varies as shown. (2)

📚 Jan 2022

• There must be more mass (than we can observe) [Accept statement that there must be a greater gravitational force]
• There is dark matter present (in the galaxy)

Describe what is meant by dark matter (2)

📚 Jan 2023

• Dark matter has mass Or Dark matter exerts a gravitational force
• Dark matter does not emit electromagnetic radiation

The orbital period of the star is actually 6.0 * 10^7s (smaller). Deduce what this tells us about our galaxy. Assume that the value for the distance of the star from the centre of our galaxy is correct (4)

📚 Jun 2024

• The actual period is (much) smaller than the calculated value
• So the mass of the galaxy must be greater than 8.0 × 10^11 solar masses [accept the given mass for the numerical value] Or the gravitational force on the star must be bigger (than assumed)
• There must be matter that does not emit em-radiation Or There must be matter that we cannot detect via em-radiation [Accept “there must be matter that we cannot see”]
• (This suggests that) there is dark matter

The observed variation of v with r has been added to produce the graph below. Suggest why the “observed” velocity varies as shown. (2)

📚 Jan 2022

• There must be more mass (than we can observe) [Accept statement that there must be a greater gravitational force]
• There is dark matter present (in the galaxy)

Falling asteroids

Explain why the mass of the asteroid would not remain constant as the asteroid fell to the surface of the earth (2)

📚 Oct 2023

• Work would be done on the asteroid by frictional forces Or Drag/friction causes heating (of the asteroid)
• Asteroid burns up

Astronauts

Explain why astronauts may be described as “weightless” (2)

📚 Jan 2024

• The astronauts must experience a centripetal force as they orbit the Earth Or The weight of the astronaut acts as a centripetal force Or The astronauts are in free fall as they orbit the Earth
• They do not experience (normal) contact forces

Gravitational fields

Explain why equipotential surfaces are not equally spaced (2)

📚 Jun 2024

• \(V_{\text{grav}} = -\frac{GM}{r}\), so gravitational potential \(\propto\frac{1}{r}\) Or \(V_{\text{grav}} = -\frac{GM}{r}\) and \(G\) and \(M\) are constant
• The equipotential surfaces become further apart with increasing distance (from Earth)

parallax angles

Describe how trigonometric parallax can be used to determine the distance to a nearby star (3)

📚 Oct 2021

• Find (angular) displacement of the star (as Earth moves around the Sun) over a 6 month period Or find (angular) displacement of the star (as Earth moves around the Sun) over a diameter of the Earth’s orbit
• Measurements are made against the background of (more) distant stars
• Radius/diameter of the Earth’s orbit about the Sun must be known/measured (to calculate the distance to the star)
• [For full credit, it must be clear that angles are being measured]
• [Marks can be obtained from an annotated diagram]

Wien's Law

At this stage of its evolution the Sun will be classified as a red giant star. The wavelength of the red light is between \(6.2\times10^{-7}m\) and \(6.2\times10^{-7}m\). COMMENT on the value for lambda_max and this classification of the Sun (3)

📚 Oct 2021

• \(λ_{\text{max}}\) is not in the wavelength range for red light Or \(λ_{\text{max}}\) is in the infrared wavelength range
• There is a range of wavelengths emitted around the value of \(λ_{\text{max}}\)
• The most intense region of the visible spectrum will be red light (dependent upon MP2)
• [Accept annotated sketches of the black body curve]

Satellite orbits

It is suggested that the satellite could be placed in an equatorial orbit at a radius of 42200 km. With this radius the satellite would have an orbital period equal to 24 hours. Give 1 advantage and 1 disadvantage of placing a weather satellite in a polar orbit rather than in the suggested equatorial orbit (2)

📚 Oct 2021

• Advantage:
• satellite can cover more of the Earth’s surface
• satellite passes close to the polar regions
• better resolution, as satellite closer to the Earth
• Disadvantage:
• satellite has to be tracked in the sky
• satellite data cannot be received continuously
• cannot provide continuous viewing of a single location

standard candles

State what is meant by a standard candle (1)

📚 Jun 2021

• A standard candle is a (astronomical) object of known luminosity

Inverse square law

Explain why the acceleration increases as time passes (2)

📚 Jan 2021

• The force between the galaxies obeys the inverse square law Or F=Gm1M2/r^2 or F is directly proportional to 1/r^2
• F = ma, so as the (resultant) force increases, so does the acceleration

Dust in space around a star may affect how bright the star appears to be. It is claimed that dust around a standard candle would lead to the conclusion that the standard candle is a greater distance from Earth than the actual distance. Access the validity of this claim. (3)

📚 Jan 2021

• A layer of dust around the candle would reduce the intensity
• Intensity obeys an inverse square law Or I = L/4pi*d^2(symbol I or L defined)
• A smaller value of intensity would lead to larger (calculated) distance, so claim is valid

State why this expression (\(mgΔh\)) cannot be used to calculate the change in gravitational potential energy of the satellite (1)

📚 Jun 2020

• (The graph shows) g is not constant (from the surface of the Earth to height of 5RE) Or the gravitational field is not uniform over this distance

Inferences question

Explain why Salyut 1 burned up (2)

📚 Jan 2021

• A (large) drag force acted on the satellite
• Work is done on satellite (by drag force) and temperature of satellite increases
• OR
• Air in front of satellite is compressed
• Energy is transferred to satellite (from hot air) and temperature of satellite increases

H-R diagram and age of star

*The appearance of the HR diagram changes as stars in the cluster evolve. Explain the changes in the appearance of the HR diagram as the star cluster gets older (6)

📚 Jan 2021

• IC1 When hydrogen fusion ends main sequence stars evolve into red giant stars
• IC2 This happens first for stars near the top of the main sequence Or this happens first for the (most) massive main sequence stars
• IC3 Red giant stars are located above the main sequence
• IC4 When helium fusion ends red giant stars evolve into white dwarf stars
• IC5 White dwarf stars are located below the main sequence
• IC6 Red giant stars are larger (in surface area) and have a lower (surface) temperature Or White dwarf stars are smaller (in surface area) and have a higher (surface) temperature

Electric fields VS gravitational fields

Give 1 similarity and 1 difference between electric fields and gravitational fields (2)

📚 Jun 2020

• Similarity:
• Both fields obey an inverse square law (for point masses/charges) Or both fields have an infinite range
• Difference:
• Electric fields can be attractive or repulsive, whereas gravitational fields can only be attractive Or electric fields exert forces on charges whereas gravitational fields exert forces on masses

Miscellaneous

1.4 Materials

Explain how the airship is able to float in the air (2)

📚 Jun 2022

• Upthrust on airship is equal to the weight of the airship (so) resultant force on the airship is zero (so airship floats in the air)
• Or (vertically) balanced forces act on the airship

State what is meant by an elastic material (1)

📚 Jan 2021

• Material returns to its original shape (and size) once (deforming) force removed

1.3 Mechanics

If the amplitude of oscillation is large enough, the man will lose contact with the board at a point above the equilibrium position. Explain why. (3)

📚 Jun 2022

• The resultant force on the man = \(mg – R\) where \(R\) is the (normal) contact force from the board
• R decreases as his displacement (from the equilibrium position) increases
• Man loses contact with board when \(R = 0\) Or Man loses contact with board when resultant force on man is equal to his weight
• OR
• Acceleration (for SHM) increases as displacement increases
• Maximum (downward) acceleration of man is \(g\)
• Man loses contact with board when acceleration of the board is equal to \(g\)

4.4 Electric and Magnetic Fields

Explain how alternating current in the coil causes the cone to oscillate with the frequency of the alternating current (3)

📚 Jan 2022

• Either
• Current carrying coil/conductor in a magnetic field
• Coil experiences a force
• Force changes direction with current (as current is changing direction)
• Or
• Current in coil causes a magnetic field
• Field interacts with permanent magnet's field, so force on coil
• Field changes direction with current so force changes direction

Advantage of data logger

In some experiments, it is an advantage to use a data logger rather than other measuring experiments. Describe when the use of a data logger is an advantage (2)

📚 Jun 2021

• EITHER
• Suitable data logger application identified
• Reason why data logger is an advantage in this situation
• OR Max 2 from
• When data has to be collected over a very short time interval
• When multiple data sets have to be collected simultaneously
• When data has to be collected over a very long time interval

4.4 Electric and Magnetic Field

State how ions of this energy (245 MeV) could be produced (1)

📚 Jun 2020

• Cyclotron Or Linac Or Particle accelerator