ESAT Physics: Waves and radioactivity, set 1

• Answer all questions. No calculator.
• Each question has exactly one correct answer.

1. 11 mark

   A wave travelling across the surface of a pond has a wavelength of 2.5 m and a frequency of 4 Hz. What is the speed of the wave?

   1. A 0.625 m/s
   2. B 40 m/s
   3. C 6.5 m/s
   4. D 10 m/s
2. 21 mark

   A sound wave travelling through air consists of regions where air particles are pushed closer together and regions where they are spread further apart. Which pair of terms correctly names these two regions, and what type of wave is this an example of?

   1. A Peak and trough; a transverse wave, because the particles vibrate perpendicular to the direction of energy transfer.
   2. B Peak and trough; a longitudinal wave, because the particles vibrate parallel to the direction of energy transfer.
   3. C Compression and rarefaction; a transverse wave, because the particles vibrate perpendicular to the direction of energy transfer.
   4. D Compression and rarefaction; a longitudinal wave, because the particles vibrate parallel to the direction of energy transfer.
3. 31 mark

   An ambulance siren is heard by a stationary bystander as the ambulance approaches, passes, and then moves away. Which statement correctly describes what the bystander hears, and why?

   1. A The pitch is higher as the ambulance approaches and lower as it moves away, because the wavefronts are compressed in front of the moving source and stretched out behind it.
   2. B The pitch stays the same throughout, but the volume changes, because the Doppler effect only affects amplitude, not frequency.
   3. C The pitch is lower as the ambulance approaches and higher as it moves away, because the wavefronts are stretched out in front of the moving source and compressed behind it.
   4. D The pitch is higher throughout while the ambulance is moving, then suddenly returns to normal the instant it passes, because the frequency emitted by the siren itself changes as it moves.
4. 41 mark

   A ray of light strikes a plane mirror, making an angle of 35 degrees with the mirror surface. What is the angle of reflection, measured from the normal?

   1. A 35 degrees
   2. B 55 degrees
   3. C 90 degrees
   4. D 70 degrees
5. 51 mark

   A ray of light travels from air into glass, hitting the boundary at an angle to the normal. Glass is optically denser than air. Which statement correctly describes what happens to the ray's speed and its direction at the boundary?

   1. A The light speeds up and bends towards the normal, because it is entering an optically denser medium.
   2. B The light slows down and bends towards the normal, because it is entering an optically denser medium.
   3. C The light slows down and bends away from the normal, because it is entering an optically denser medium.
   4. D The light's speed and direction are unchanged, because refraction only affects the wavelength of light, not its speed or direction.
6. 61 mark

   Which statement about sound waves is correct?

   1. A Sound waves are longitudinal waves that require a medium to travel through, and cannot travel through a vacuum.
   2. B Sound waves are transverse waves that require a medium to travel through, and cannot travel through a vacuum.
   3. C Sound waves are longitudinal waves that can travel through a vacuum as well as through solids, liquids and gases.
   4. D Sound waves are longitudinal waves that require a medium, but travel fastest through a vacuum because there are no particles to slow them down.
7. 71 mark

   The electromagnetic spectrum is arranged in order of increasing frequency as: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Which of these types of electromagnetic wave has the longest wavelength?

   1. A Microwaves
   2. B Visible light
   3. C Radio waves
   4. D Gamma rays
8. 81 mark

   Which type of electromagnetic wave is most associated with an increased risk of skin cancer from overexposure, and why?

   1. A Infrared, because it carries enough energy to damage the DNA in skin cells.
   2. B Ultraviolet, because it carries enough energy to damage the DNA in skin cells.
   3. C Microwaves, because they cause ionisation in the cells they pass through.
   4. D Radio waves, because their long wavelength allows them to penetrate deep into the body and damage internal organs.
9. 91 mark

   An atom of a particular element has a mass number of 23 and an atomic number of 11. How many protons, neutrons and electrons does a neutral atom of this element contain?

   1. A 11 protons, 23 neutrons, 11 electrons
   2. B 11 protons, 12 neutrons, 23 electrons
   3. C 23 protons, 11 neutrons, 23 electrons
   4. D 11 protons, 12 neutrons, 11 electrons
10. 101 mark

    Two atoms of the same element, carbon-12 and carbon-14, are isotopes of each other. Which statement correctly explains what this means?

    1. A They have different numbers of protons and different numbers of neutrons, but happen to be the same element by coincidence.
    2. B They have the same number of neutrons but different numbers of protons, giving them different atomic numbers but the same mass number.
    3. C They have the same number of protons but different numbers of neutrons, giving them different mass numbers but the same atomic number.
    4. D They have the same number of protons and the same number of neutrons, but different numbers of electrons, giving them different overall charges.
11. 111 mark

    A nucleus of uranium-238 (atomic number 92) undergoes alpha decay. What are the mass number and atomic number of the daughter nucleus produced?

    1. A Mass number 234, atomic number 92
    2. B Mass number 238, atomic number 93
    3. C Mass number 234, atomic number 90
    4. D Mass number 236, atomic number 90
12. 121 mark

    Which statement correctly describes beta decay?

    1. A A proton in the nucleus changes into a neutron, releasing an electron as the beta particle; the atomic number decreases by 1 while the mass number stays the same.
    2. B The nucleus emits two protons and two neutrons bound together as a single particle, decreasing both the mass number and the atomic number.
    3. C A neutron in the nucleus changes into a proton and an electron; the electron is emitted as a beta particle, and the mass number increases by 1 while the atomic number stays the same.
    4. D A neutron in the nucleus changes into a proton and an electron; the electron is emitted as a beta particle, and the atomic number increases by 1 while the mass number stays the same.
13. 131 mark

    Alpha, beta and gamma radiation are each passed through a strong magnetic field. Which statement correctly compares how they are affected?

    1. A Alpha and beta particles are deflected in the same direction because they are both charged, while gamma radiation is deflected the most because it carries the most energy.
    2. B None of the three types are deflected by a magnetic field, because ionising radiation is not affected by electric or magnetic fields.
    3. C All three types are deflected by the same amount in a magnetic field, because a magnetic field affects the path of any moving radiation regardless of charge.
    4. D Alpha and beta particles are deflected in opposite directions because they carry opposite charges, while gamma radiation is undeflected because it is uncharged.
14. 141 mark

    A sample of a radioactive isotope has a half-life of 8 days. If the initial activity of the sample is 800 Bq, what will the activity be after 24 days?

    1. A 0 Bq
    2. B 200 Bq
    3. C 100 Bq
    4. D 50 Bq
15. 151 mark

    A graph shows the activity of a radioactive sample falling from an initial value of 480 Bq. A line drawn from 480 Bq down to half that value (240 Bq), then across to the time axis, gives a time of 5 minutes. What is the half-life of the sample, and what will its activity be after a further 5 minutes have passed (10 minutes after the start)?

    1. A Half-life = 5 minutes; activity after 10 minutes = 120 Bq.
    2. B Half-life = 5 minutes; activity after 10 minutes = 240 Bq.
    3. C Half-life = 10 minutes; activity after 10 minutes = 240 Bq.
    4. D Half-life = 5 minutes; activity after 10 minutes = 0 Bq.

Worked solutions

Every question below carries the reasoning, not just the answer. The official material for this test publishes a correct option letter and nothing else.

1. Question 1Answer: D

   1. Wave speed is calculated using wave speed = frequency x wavelength.
   2. Substituting the given values: wave speed = 4 Hz x 2.5 m.
   3. 4 x 2.5 = 10, so the wave speed is 10 m/s.
   4. The answer is D.
   • Why not A: This divides wavelength by frequency (2.5 / 4) rather than multiplying, using the inverted relationship wave speed = wavelength / frequency instead of wave speed = frequency x wavelength.
   • Why not B: This squares the frequency before multiplying (4^2 x 2.5) rather than using the frequency to the first power, a slip that confuses the wave speed equation with a squared relationship.
   • Why not C: This adds the frequency and wavelength (4 + 2.5) instead of multiplying them, treating wave speed as a sum of the two quantities rather than their product.

2. Question 2Answer: D

   1. Sound waves are produced by particles vibrating parallel to (along) the same direction that the wave's energy travels, which is the definition of a longitudinal wave.
   2. In a longitudinal wave, the regions where particles are pushed closer together are called compressions, and the regions where they are spread further apart are called rarefactions.
   3. The terms peak and trough describe the highest and lowest displacement points of a transverse wave, where particles vibrate perpendicular to the direction of energy transfer, so they do not apply here.
   4. The wave described is therefore longitudinal, with compressions and rarefactions, so the answer is D.
   • Why not A: This combines two errors at once: it uses the transverse-wave terms peak and trough for a wave whose particles vibrate parallel to the direction of travel, and it misclassifies that parallel vibration as transverse rather than longitudinal.
   • Why not B: This correctly identifies sound as longitudinal but wrongly borrows the terms peak and trough, which describe the highest and lowest displacement points of a transverse wave; a longitudinal wave has compressions and rarefactions instead.
   • Why not C: This uses the correct terms compression and rarefaction but wrongly calls the wave transverse; in a longitudinal wave the particles vibrate parallel to (along) the direction of energy transfer, not perpendicular to it, which is the defining feature of a transverse wave.

3. Question 3Answer: A

   1. The Doppler effect describes how the observed frequency of a wave changes when there is relative motion between the source and the observer.
   2. As the ambulance approaches, each successive wavefront is emitted from a position closer to the bystander than the last, compressing the wavefronts and shortening the observed wavelength, so the observed frequency (pitch) increases.
   3. As the ambulance moves away, each successive wavefront is emitted further from the bystander, stretching out the wavefronts and lengthening the observed wavelength, so the observed frequency (pitch) decreases.
   4. The siren's own emitted frequency does not change; only the frequency detected by the stationary bystander changes, so the pitch is higher approaching and lower receding, meaning the answer is A.
   • Why not B: This confuses the Doppler effect, which is a shift in observed frequency (pitch) due to relative motion, with a change in amplitude (loudness); the amplitude does change with distance, but the Doppler effect specifically describes the pitch shift, not a volume-only effect.
   • Why not C: This reverses the direction of the effect: a source moving towards an observer compresses the wavefronts ahead of it (raising the observed frequency), not behind it, so the described pattern is backwards.
   • Why not D: This wrongly assumes the siren itself changes the frequency it emits; in the Doppler effect the source emits a constant frequency throughout, and it is the observer's changing distance from a moving source that changes the frequency they detect, with a gradual change as the source passes rather than a sudden jump.

4. Question 4Answer: B

   1. The law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal, the line perpendicular to the mirror surface at the point where the ray strikes it.
   2. The ray makes an angle of 35 degrees with the mirror surface itself, not with the normal, so this must be converted: the angle from the normal is 90 - 35 = 55 degrees.
   3. Since the angle of incidence (from the normal) is 55 degrees, the angle of reflection (from the normal) is also 55 degrees, by the law of reflection.
   4. The answer is B.
   • Why not A: This takes the angle measured from the mirror surface (35 degrees) as if it were already the angle of incidence; the angle of incidence and angle of reflection are conventionally measured from the normal, not from the surface, so the surface angle must first be converted using 90 - 35.
   • Why not C: This assumes the reflected ray travels straight back along the normal, making a right angle with the mirror surface regardless of the angle the incoming ray actually makes; it ignores the given 35 degree angle entirely.
   • Why not D: This doubles the given surface angle (35 x 2 = 70). It happens to equal the total angle turned by the ray between its incident and reflected directions, but the question asks for the angle of reflection measured from the normal, which is 55 degrees, not the total deviation of the ray's path.

5. Question 5Answer: B

   1. Refraction occurs when a wave crosses a boundary between two media in which it travels at different speeds.
   2. Glass is optically denser than air, so light travels more slowly in glass than in air; the ray therefore slows down as it crosses from air into glass.
   3. When a wave slows down on crossing into a denser medium, it bends towards the normal, the line perpendicular to the boundary at the point of incidence.
   4. So the light slows down and bends towards the normal, meaning the answer is B.
   • Why not A: This gets the speed change backwards: light travels more slowly in an optically denser medium such as glass than in air, not more quickly, even though it correctly states that the ray bends towards the normal.
   • Why not C: This gets the direction of bending backwards: light bends towards the normal when entering an optically denser medium, where it slows down; it only bends away from the normal when entering a less dense medium, where it speeds up.
   • Why not D: This assumes refraction leaves speed and direction unchanged and only affects wavelength; in fact refraction changes the wave's speed and, except at normal incidence, its direction as it crosses the boundary. The frequency stays constant and the wavelength changes as a consequence of the speed change, not instead of it.

6. Question 6Answer: A

   1. Sound is produced by a vibrating source, such as a loudspeaker cone or a vocal cord, which pushes on the particles of the surrounding medium.
   2. These vibrations pass from particle to particle, with each particle vibrating parallel to the direction the wave travels, which is the definition of a longitudinal wave, producing compressions and rarefactions.
   3. Because sound relies on particles colliding with their neighbours to pass the vibration along, it needs a medium (a solid, liquid or gas) and cannot travel through the particle-free vacuum of space.
   4. Sound waves are therefore longitudinal and require a medium, so the answer is A.
   • Why not B: Sound waves are longitudinal, not transverse: the particles of the medium vibrate parallel to the direction the wave travels, creating compressions and rarefactions, not perpendicular to it as in a transverse wave.
   • Why not C: Sound requires particles in a medium to pass the vibration from one particle to the next; a vacuum contains no particles, so sound cannot travel through it at all, unlike electromagnetic waves such as light.
   • Why not D: This combines two errors: it wrongly claims sound needs a medium but travels fastest with no particles present. A vacuum contains no particles at all, so sound cannot travel through it, let alone faster than through a solid, liquid or gas.

7. Question 7Answer: C

   1. All electromagnetic waves travel at the same speed in a vacuum (the speed of light), and wave speed = frequency x wavelength, so for a fixed speed, wavelength and frequency vary inversely.
   2. The spectrum is ordered by frequency as: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays, from lowest frequency to highest.
   3. Since wavelength decreases as frequency increases, the wave with the lowest frequency has the longest wavelength; radio waves have the lowest frequency of the list.
   4. Radio waves therefore have the longest wavelength, so the answer is C.
   • Why not A: Microwaves have a longer wavelength than infrared, visible light, ultraviolet, X-rays and gamma rays, but radio waves sit below microwaves in frequency and therefore have an even longer wavelength; microwaves are not the longest-wavelength type in the full spectrum.
   • Why not B: Visible light sits in the middle of the spectrum, with radio waves, microwaves and infrared all having longer wavelengths than it, so it cannot be the longest-wavelength type.
   • Why not D: Gamma rays have the highest frequency of any electromagnetic wave, and frequency and wavelength are inversely related for waves travelling at the same speed, so gamma rays have the shortest wavelength, not the longest.

8. Question 8Answer: B

   1. The hazard a type of electromagnetic wave poses depends on how much energy it carries and how that energy affects living tissue, which generally increases with frequency across the spectrum.
   2. Ultraviolet radiation has a high enough frequency, and therefore enough energy, to be absorbed by skin cells and damage the DNA within them.
   3. This DNA damage is what increases the risk of skin cancer with excessive exposure to ultraviolet radiation, such as from the Sun or sunbeds.
   4. The answer is B.
   • Why not A: Infrared radiation carries less energy than ultraviolet and is mainly associated with heating effects on the skin, not with damaging DNA; it is ultraviolet's higher energy and shorter wavelength that allow it to break chemical bonds in skin cell DNA.
   • Why not C: Microwaves are non-ionising: they carry too little energy per photon to remove electrons from atoms or break chemical bonds such as those in DNA. Their main hazard is internal heating of tissue, not ionisation.
   • Why not D: Radio waves have the lowest energy and longest wavelength in the electromagnetic spectrum; they do not carry enough energy to damage DNA, and this is not the mechanism linked to the skin cancer risk of ultraviolet exposure.

9. Question 9Answer: D

   1. The atomic number gives the number of protons in the nucleus, so this atom has 11 protons.
   2. The mass number gives the total number of protons and neutrons, so the number of neutrons is mass number minus atomic number: 23 - 11 = 12 neutrons.
   3. A neutral atom has no overall charge, so the number of electrons equals the number of protons: 11 electrons.
   4. The atom therefore has 11 protons, 12 neutrons and 11 electrons, so the answer is D.
   • Why not A: This takes the mass number itself as the number of neutrons, forgetting that mass number = number of protons + number of neutrons; the neutron count must be found by subtracting the atomic number (protons) from the mass number, giving 23 - 11 = 12, not 23.
   • Why not B: This correctly finds the proton and neutron counts but then sets the electron count equal to the mass number instead of the proton count; a neutral atom has equal numbers of protons and electrons, so it should have 11 electrons, not 23.
   • Why not C: This swaps the atomic number and mass number, treating the mass number (23) as the proton count and the atomic number (11) as the neutron count; the atomic number always gives the number of protons, and the mass number is the total of protons and neutrons.

10. Question 10Answer: C

    1. Isotopes are atoms of the same element, so by definition they must have the same number of protons (the same atomic number).
    2. What differs between isotopes is the number of neutrons in the nucleus, which changes the total mass number (protons plus neutrons) but not the atomic number.
    3. Carbon-12 has 6 protons and 6 neutrons (mass number 12), while carbon-14 has 6 protons and 8 neutrons (mass number 14); both have atomic number 6, confirming they are both carbon.
    4. So isotopes share the same atomic number but have different mass numbers due to different neutron numbers, meaning the answer is C.
    • Why not A: Atoms of the same element must have the same number of protons by definition; if the number of protons differed, the atoms would be different elements entirely, not isotopes of the same one.
    • Why not B: This swaps protons and neutrons: it is the number of protons (the atomic number) that defines which element an atom is and that must be the same for isotopes of that element; the number of neutrons is what varies between isotopes, not what stays fixed.
    • Why not D: This describes ions, not isotopes: an ion forms when an atom gains or loses electrons, changing its charge, while the number of protons and neutrons in the nucleus stays the same. Isotopes have identical proton numbers but different neutron numbers, with the electron count unaffected.

11. Question 11Answer: C

    1. An alpha particle is identical to a helium nucleus: it has a mass number of 4 and an atomic number of 2.
    2. When a nucleus emits an alpha particle, it loses 4 from its mass number and 2 from its atomic number, because those nucleons leave with the alpha particle.
    3. Starting from uranium-238 (atomic number 92): mass number = 238 - 4 = 234, and atomic number = 92 - 2 = 90.
    4. The daughter nucleus has mass number 234 and atomic number 90, so the answer is C.
    • Why not A: This correctly subtracts the alpha particle's mass number (4) from 238 to get 234, but forgets that the atomic number also decreases in alpha decay; an alpha particle carries away 2 protons, so the atomic number must fall from 92 to 90, not stay at 92.
    • Why not B: This applies the rule for beta decay, where the mass number is unchanged and the atomic number increases by 1 as a neutron converts to a proton, to a question about alpha decay; in alpha decay the nucleus emits a helium nucleus, so both the mass number (down by 4) and the atomic number (down by 2) decrease.
    • Why not D: This subtracts the alpha particle's atomic number (2) from the parent's mass number, instead of the alpha particle's own mass number (4); an alpha particle has a mass number of 4, so 4 must be subtracted from 238 to give 234, not 236.

12. Question 12Answer: D

    1. In beta decay, a neutron inside the nucleus converts into a proton and an electron.
    2. The newly created electron is emitted from the nucleus at high speed as a beta particle, while the proton remains in the nucleus.
    3. Because a neutron has become a proton, the number of protons (the atomic number) increases by 1, but the total number of nucleons (protons plus neutrons) is unchanged, so the mass number stays the same.
    4. This matches the description in option D, so the answer is D.
    • Why not A: This has proton and neutron the wrong way round: in beta decay it is a neutron that converts into a proton, not a proton into a neutron, and the electron produced is emitted as the beta particle. Because a neutron becomes an additional proton, the atomic number increases by 1; it does not decrease.
    • Why not B: This describes alpha decay, where the nucleus emits two protons and two neutrons bound together as a helium nucleus, reducing both the mass number and the atomic number; beta decay involves no proton or neutron leaving the nucleus, only a neutron converting into a proton with an electron emitted.
    • Why not C: This has the two nuclear numbers the wrong way round: in beta decay, a neutron converting into a proton increases the number of protons, so the atomic number increases by 1; the total number of nucleons in the nucleus is unchanged, so the mass number stays the same, not the other way round.

13. Question 13Answer: D

    1. A magnetic field exerts a force on a moving charged particle, deflecting its path; the direction of deflection depends on the sign of the charge, and gamma radiation carries no charge at all.
    2. Alpha particles are positively charged (they are helium nuclei), and beta particles are negatively charged (they are fast-moving electrons), so a magnetic field deflects them in opposite directions from one another.
    3. Gamma radiation is electromagnetic radiation with no charge, so it is unaffected by a magnetic field and travels straight through undeflected.
    4. The answer is D.
    • Why not A: This wrongly claims alpha and beta particles deflect the same way; a magnetic field deflects a moving charge in a direction that depends on the sign of the charge, and since alpha particles are positive while beta particles are negative, they curve in opposite directions. It also wrongly gives gamma radiation the largest deflection, when gamma radiation carries no charge and is not deflected by a magnetic field at all.
    • Why not B: Alpha particles (positively charged) and beta particles (negatively charged) are both charged particles, and a moving charged particle experiences a force in a magnetic field; only gamma radiation, which is uncharged, passes through without being deflected.
    • Why not C: A magnetic field only exerts a force on a moving charged particle; gamma radiation is uncharged (it is electromagnetic radiation, not a stream of charged particles), so it passes through undeflected while alpha and beta, which are charged, are deflected.

14. Question 14Answer: C

    1. The number of half-lives that have passed is the total time divided by the half-life: 24 days / 8 days per half-life = 3 half-lives.
    2. Each half-life, the activity halves: starting at 800 Bq, after 1 half-life it is 400 Bq, after 2 half-lives it is 200 Bq, and after 3 half-lives it is 100 Bq.
    3. So after 24 days (3 half-lives), the activity has fallen to 100 Bq.
    4. The answer is C.
    • Why not A: This assumes that after a whole number of half-lives the sample has completely decayed to zero activity; in reality, activity halves repeatedly but never reaches exactly zero. After 3 half-lives the activity is one eighth of the original (800 / 8 = 100 Bq), not zero.
    • Why not B: This stops one half-life early: 24 days is 24 / 8 = 3 half-lives, so the activity must be halved three times (800 -> 400 -> 200 -> 100), not two times (800 -> 400 -> 200).
    • Why not D: This uses one half-life too many: 24 days corresponds to 24 / 8 = 3 half-lives, not 4, so the activity should be halved three times (giving 100 Bq), not four times (which would give 50 Bq).

15. Question 15Answer: A

    1. The half-life is the time taken for the activity of a radioactive sample to fall to half of its value; the graph shows activity falling from 480 Bq to 240 Bq (exactly half) in 5 minutes, so the half-life is 5 minutes.
    2. A further 5 minutes brings the total elapsed time to 10 minutes, which is 10 / 5 = 2 half-lives.
    3. Each half-life halves the activity: after 1 half-life (5 minutes) the activity is 480 / 2 = 240 Bq, and after 2 half-lives (10 minutes) it is 240 / 2 = 120 Bq.
    4. The half-life is therefore 5 minutes and the activity after 10 minutes is 120 Bq, so the answer is A.
    • Why not B: This correctly finds the half-life of 5 minutes but forgets that a further 5 minutes means a second half-life has now passed since the start (10 minutes in total); it repeats the activity at the 5 minute mark (240 Bq) instead of halving again to reach the activity at 10 minutes.
    • Why not C: This misreads the graph: the point plotted is where the activity has fallen to half its initial value (240 Bq out of 480 Bq), which is exactly the definition of the half-life, so the half-life is 5 minutes, not 10. It also only applies one halving to the full 10 minute period, when two half-lives have actually passed.
    • Why not D: This correctly finds the half-life but wrongly assumes the sample's activity falls to zero after two half-lives; activity halves repeatedly and never reaches exactly zero. After 2 half-lives, the activity is one quarter of the original: 480 / 4 = 120 Bq, not 0 Bq.