ESAT Physics: Waves and radioactivity, set 2

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

1. 11 mark

   A wave has a period of 0.02 s and a wavelength of 3.4 m. What is its speed?

   1. A 0.068 m/s
   2. B 1.7 m/s
   3. C 170 m/s
   4. D 53.4 m/s
2. 21 mark

   A wave travelling in one medium reflects off a flat surface and returns through the same medium. Which statement correctly describes what happens to the wave's speed, frequency and wavelength as a result of this reflection?

   1. A Speed, frequency and wavelength all stay the same; only the direction of travel changes.
   2. B Frequency decreases upon reflection, while speed and wavelength stay the same, because the wave loses energy to the surface it reflects from.
   3. C Speed decreases upon reflection, while frequency and wavelength stay the same, because the wave has changed direction.
   4. D Wavelength increases upon reflection, while speed and frequency stay the same, because the reflected wave now has further to travel to reach an observer.
3. 31 mark

   A loudspeaker emits a sound wave with a frequency of 25 kHz. Which statement about this wave is correct?

   1. A The wave is within the range of human hearing, since 25 kHz is close to the upper limit of 20 kHz.
   2. B The wave is infrasound, since it has an unusually high frequency for a sound wave.
   3. C The wave cannot exist, since sound waves are not able to have frequencies above 20 kHz.
   4. D The wave is ultrasound, since its frequency is above the upper limit of human hearing (20 kHz); waves like this are used in applications such as sonar and medical scanning.
4. 41 mark

   A ray of light reflects from a plane mirror. The angle between the incident ray and the reflected ray, measured at the point of reflection, is 80 degrees. What is the angle of incidence, measured from the normal?

   1. A 80 degrees
   2. B 40 degrees
   3. C 10 degrees
   4. D 50 degrees
5. 51 mark

   A ray of light travels from glass into air, 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 direction as it crosses the boundary?

   1. A The light speeds up and bends away from the normal, because it is leaving an optically denser medium for a less dense one.
   2. B The light slows down and bends away from the normal, because it is leaving an optically denser medium for a less dense one.
   3. C The light speeds up and bends towards the normal, because it is leaving an optically denser medium for a less dense one.
   4. D The light slows down and bends towards the normal, because light entering a new medium always slows down and bends towards the normal.
6. 61 mark

   Which of the following correctly matches an application to gamma radiation, together with the reason gamma radiation is suitable for it?

   1. A Satellite communication and cooking food, because gamma radiation is strongly absorbed by water molecules.
   2. B Medical imaging of bones and airport security scanning, because gamma radiation passes through soft tissue but is absorbed by denser materials such as bone or metal.
   3. C Sterilising medical instruments and treating cancerous tumours, because gamma radiation is highly ionising and can kill living cells.
   4. D Remote controls and thermal imaging cameras, because gamma radiation is emitted by all objects according to their temperature.
7. 71 mark

   A wave source produces 15 complete oscillations in 3 seconds. What is the period of the wave?

   1. A 5 s
   2. B 3 s
   3. C 0.6 s
   4. D 0.2 s
8. 81 mark

   A sound wave's amplitude is increased while its frequency stays exactly the same. Which statement correctly describes the effect on the sound heard?

   1. A The sound becomes higher in pitch, but the loudness stays the same, because increasing amplitude increases frequency.
   2. B The sound becomes louder, but the pitch stays the same, because loudness depends on amplitude and pitch depends on frequency.
   3. C The sound becomes quieter, because a sound wave with a larger amplitude loses its energy more quickly as it travels.
   4. D Both the loudness and the pitch increase, because amplitude and frequency always increase together.
9. 91 mark

   An atom has a nucleon number of 32 and a proton number of 16. It gains 2 electrons to form an ion. How many protons, neutrons and electrons does the resulting ion contain?

   1. A 16 protons, 16 neutrons, 14 electrons
   2. B 18 protons, 16 neutrons, 16 electrons
   3. C 16 protons, 16 neutrons, 18 electrons
   4. D 16 protons, 32 neutrons, 18 electrons
10. 101 mark

    A neutral atom loses two electrons. What is the overall charge of the resulting ion, and why?

    1. A 2+, because the atom now has two more protons than electrons, giving it a net positive charge.
    2. B 2-, because losing electrons increases the negative charge of the atom.
    3. C Neutral, because the numbers of protons and neutrons in the nucleus are unaffected by the loss of electrons.
    4. D 1+, because only one of the two lost electrons actually contributes to the ion's charge.
11. 111 mark

    A nucleus of carbon-14 (atomic number 6) undergoes beta decay. What are the mass number and atomic number of the nucleus produced?

    1. A Mass number 13, atomic number 7
    2. B Mass number 14, atomic number 7
    3. C Mass number 14, atomic number 5
    4. D Mass number 10, atomic number 4
12. 121 mark

    A nucleus with mass number 214 and atomic number 82 decays into a nucleus with mass number 214 and atomic number 83. Which type of decay has occurred?

    1. A Alpha decay
    2. B Gamma emission alone
    3. C Emission of a proton
    4. D Beta decay
13. 131 mark

    Which material is sufficient on its own to completely stop alpha radiation, but does not stop beta or gamma radiation?

    1. A A sheet of paper
    2. B A few millimetres of aluminium
    3. C A thick sheet of lead
    4. D No material can stop alpha radiation, since it is highly penetrating
14. 141 mark

    Which of the following is a natural source of background radiation?

    1. A X-rays used during a hospital scan
    2. B Fallout from past nuclear weapons testing
    3. C Radon gas seeping out of rocks in the ground
    4. D Radioactive waste stored at a nuclear power station
15. 151 mark

    A sample of radioactive material has a half-life of 5 hours. If the initial mass of undecayed nuclei is 480 g, what mass of undecayed nuclei remains after 20 hours?

    1. A 60 g
    2. B 30 g
    3. C 0 g
    4. D 15 g

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: C

   1. Frequency is the reciprocal of the period: frequency = 1 / period = 1 / 0.02 = 50 Hz.
   2. Wave speed is found using wave speed = frequency x wavelength.
   3. Substituting the values: wave speed = 50 Hz x 3.4 m = 170 m/s.
   4. The answer is C.
   • Why not A: This multiplies the wavelength by the period itself (3.4 x 0.02) rather than first finding the frequency; frequency is the reciprocal of the period (1 / 0.02 = 50 Hz), not the period value used directly in the wave speed equation.
   • Why not B: This finds the reciprocal of the period but misplaces the decimal point, giving 0.5 Hz instead of 50 Hz, and then multiplies by the wavelength (0.5 x 3.4 = 1.7); the correct reciprocal of 0.02 is 50, not 0.5.
   • Why not D: This correctly finds the frequency (1 / 0.02 = 50 Hz) but then adds the wavelength to the frequency (50 + 3.4) instead of multiplying them, treating wave speed as a sum rather than the product of frequency and wavelength.

2. Question 2Answer: A

   1. Reflection in the same medium changes only the direction the wave is travelling; it does not change the medium the wave is passing through.
   2. Since the wave's speed depends on the medium, and the medium has not changed, the speed stays the same.
   3. Frequency is fixed by the source and does not change on reflection, and since wavelength = speed / frequency, with both speed and frequency unchanged, the wavelength is also unchanged.
   4. The answer is A.
   • Why not B: Reflection can reduce the wave's amplitude as some energy is absorbed by the surface, but this does not change its frequency; frequency is set by the source and stays constant through reflection in the same medium.
   • Why not C: The wave's speed depends on the medium it is travelling through, not on its direction; since the wave remains in the same medium after reflecting, its speed is unchanged, even though its direction has reversed.
   • Why not D: Wavelength depends only on the wave's speed and frequency (wavelength = speed / frequency), not on how far the wave still has to travel to reach an observer; since speed and frequency are both unchanged by reflection in the same medium, the wavelength cannot change either.

3. Question 3Answer: D

   1. The range of human hearing is 20 Hz to 20 kHz; any sound wave with a frequency outside this range is inaudible to humans but still exists as a real sound wave.
   2. A frequency of 25 kHz is above the 20 kHz upper limit of human hearing, so this wave is classed as ultrasound.
   3. Ultrasound waves like this are used in applications such as sonar (to detect objects or measure distances) and medical scanning (to image inside the body).
   4. The answer is D.
   • Why not A: 25 kHz is above the upper limit of human hearing, not merely close to it; the human hearing range extends only up to 20 kHz, so a wave at 25 kHz falls outside that range rather than within it.
   • Why not B: Infrasound refers to sound with a frequency below the lower limit of human hearing (below 20 Hz), not an unusually high frequency; a high-frequency sound wave above 20 kHz is called ultrasound, the opposite end of the spectrum.
   • Why not C: The 20 Hz to 20 kHz range describes the limits of human hearing, not a physical limit on sound waves themselves; sound waves with frequencies above 20 kHz exist and travel normally, they are simply inaudible to humans.

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 at the point of reflection.
   2. If the incident and reflected rays are drawn as two rays leaving the point of reflection, the normal lies exactly midway between them, so the angle between the two rays is twice the angle of incidence.
   3. Given that this total angle is 80 degrees, the angle of incidence = 80 / 2 = 40 degrees.
   4. The answer is B.
   • Why not A: This treats the given 80 degree angle between the two rays as if it were itself the angle of incidence, without recognising that this angle is the total angle between the incident and reflected rays, which is twice the angle of incidence from the normal.
   • Why not C: This assumes the 80 degrees is measured between the incident ray and the mirror surface rather than between the incident and reflected rays, and converts it using 90 - 80 = 10; the question instead gives the total angle between the two rays, which must be halved, not subtracted from 90.
   • Why not D: This correctly halves the 80 degrees to get 40 degrees, then wrongly converts this into an angle from the surface by computing 90 - 40 = 50; the question already asks for the angle from the normal, so this extra conversion step should not be applied.

5. Question 5Answer: A

   1. Refraction occurs because light travels at different speeds in different media; it travels more slowly in the optically denser glass than in air.
   2. As the ray leaves the glass and enters the air, it is moving into a less dense medium, so its speed increases.
   3. A wave that speeds up on crossing a boundary bends away from the normal, the line perpendicular to the boundary at the point of incidence.
   4. So the light speeds up and bends away from the normal, meaning the answer is A.
   • Why not B: This correctly identifies that the ray bends away from the normal but gets the speed change backwards: light travels more slowly in the optically denser glass than in air, so on leaving glass for air it speeds up, it does not slow down further.
   • Why not C: This correctly identifies that the light speeds up but gets the direction backwards: light bends away from the normal when it speeds up on entering a less dense medium; it only bends towards the normal when slowing down on entering a denser medium.
   • Why not D: This wrongly applies the rule for entering a denser medium (slow down, bend towards the normal) regardless of which direction the light is actually travelling; here the light is leaving the denser medium (glass) for the less dense medium (air), so it speeds up and bends away from the normal instead.

6. Question 6Answer: C

   1. Gamma radiation has a very high frequency and carries a large amount of energy per photon, making it strongly ionising.
   2. This ionising ability allows gamma radiation to damage or kill living cells, which is exploited to sterilise medical instruments (killing any bacteria present) and to destroy cancerous tumour cells in radiotherapy.
   3. The other options each describe a genuine use of a different part of the electromagnetic spectrum (microwaves, X-rays and infrared respectively), not gamma radiation.
   4. The answer is C.
   • Why not A: This describes microwaves, not gamma radiation: microwaves are strongly absorbed by water molecules, which is why they are used for satellite communication and for heating food in a microwave oven.
   • Why not B: This describes X-rays, not gamma radiation: X-rays pass more easily through soft tissue than through denser material such as bone or metal, which is why they are used for medical imaging and airport security scanning.
   • Why not D: This describes infrared radiation, not gamma radiation: all objects above absolute zero emit infrared radiation depending on their temperature, which is the basis for remote controls and thermal imaging cameras.

7. Question 7Answer: D

   1. Frequency is the number of complete oscillations per second: frequency = 15 oscillations / 3 s = 5 Hz.
   2. Period is the reciprocal of frequency: period = 1 / frequency.
   3. Substituting the frequency: period = 1 / 5 = 0.2 s.
   4. The answer is D.
   • Why not A: This correctly finds the frequency (15 oscillations / 3 s = 5 Hz) but then states this frequency value as the period itself, instead of taking its reciprocal; period and frequency are reciprocals of one another, not the same number.
   • Why not B: This takes the total time given (3 seconds) as the period directly, ignoring that 15 oscillations occurred within that time; the period is the time for one single oscillation, found by dividing the total time by the number of oscillations that occurred.
   • Why not C: This divides the total time by the frequency (3 / 5 = 0.6) rather than taking the reciprocal of the frequency (1 / 5); period and frequency are related by period = 1 / frequency, not by dividing the elapsed time by the frequency.

8. Question 8Answer: B

   1. Loudness is determined by the amplitude of a sound wave: a larger amplitude carries more energy and is heard as a louder sound.
   2. Pitch is determined by the frequency of a sound wave: a higher frequency is heard as a higher pitch.
   3. Since only the amplitude is changed here and the frequency stays the same, the loudness increases but the pitch does not change.
   4. The answer is B.
   • Why not A: This swaps which property affects which: pitch depends on frequency, not amplitude, and amplitude and frequency are independent properties of a wave, so increasing amplitude does not increase frequency or pitch.
   • Why not C: This gets the effect of amplitude backwards: a larger amplitude means the sound wave carries more energy and is heard as louder, not quieter, and amplitude alone does not determine how quickly a wave loses energy as it travels.
   • Why not D: This wrongly assumes amplitude and frequency are linked and always change together; they are independent properties of a wave, so frequency can stay exactly the same while amplitude changes, as stated in the question.

9. Question 9Answer: C

   1. The proton number of an atom does not change when it forms an ion by gaining or losing electrons, so this ion has 16 protons.
   2. The number of neutrons is the nucleon number minus the proton number: 32 - 16 = 16 neutrons.
   3. The atom gains 2 electrons, so the electron count increases from 16 (equal to the proton number in the neutral atom) to 16 + 2 = 18 electrons.
   4. The ion therefore has 16 protons, 16 neutrons and 18 electrons, so the answer is C.
   • Why not A: This subtracts the 2 gained electrons from the original electron count instead of adding them; the atom gains electrons, so its electron count should increase from 16 to 18, not decrease to 14.
   • Why not B: This wrongly adds the 2 extra electrons to the proton count instead of the electron count; gaining or losing electrons never changes the number of protons, which is fixed by the proton number of the element (16).
   • Why not D: This takes the nucleon number itself as the neutron count, forgetting that nucleon number = number of protons + number of neutrons; the correct neutron count is nucleon number minus proton number (32 - 16 = 16), not 32.

10. Question 10Answer: A

    1. An atom's overall charge is determined by the balance between its protons (positive) and electrons (negative); a neutral atom has equal numbers of each.
    2. Losing two electrons removes two units of negative charge, while the number of protons in the nucleus stays the same.
    3. The atom now has two more protons than electrons, so its overall charge is 2+.
    4. The answer is A.
    • Why not B: This gets the sign of the charge backwards: electrons carry negative charge, so losing electrons removes negative charge from the atom, leaving an excess of positive charge (from the unchanged protons), not an increased negative charge.
    • Why not C: This confuses the unchanged nucleus with the atom's overall charge; ionisation is caused by a change in the number of electrons, not protons or neutrons, and losing electrons does leave the atom with more protons than electrons, giving it a net positive charge, even though the nucleus itself is unaffected.
    • Why not D: There is no rule by which only some of the lost electrons contribute to the resulting charge; each electron carries one unit of negative charge, so losing two electrons leaves the atom two units short of negative charge, giving an overall charge of 2+, not 1+.

11. Question 11Answer: B

    1. In beta decay, a neutron inside the nucleus converts into a proton and an electron, and the electron is emitted as the beta particle.
    2. Because a neutron becomes a proton, the number of protons (the atomic number) increases by 1, from 6 to 7.
    3. The total number of nucleons in the nucleus is unchanged by this conversion, so the mass number stays the same, at 14.
    4. The nucleus produced has mass number 14 and atomic number 7, so the answer is B.
    • Why not A: This wrongly decreases the mass number by 1, as though the emitted beta particle carried away one nucleon; a beta particle is a high-speed electron with a negligible mass number, so it does not change the nucleus's mass number at all.
    • Why not C: This decreases the atomic number instead of increasing it; in beta decay a neutron converts into a proton, which increases the number of protons (the atomic number) by 1, it does not decrease it.
    • Why not D: This applies the changes for alpha decay (mass number down by 4, atomic number down by 2) rather than beta decay; alpha decay involves emitting a helium nucleus, which is not what happens in beta decay.

12. Question 12Answer: D

    1. The mass number is unchanged (214 to 214), which rules out alpha decay, since alpha decay always reduces the mass number by 4.
    2. The atomic number has increased by 1 (82 to 83), which rules out gamma emission alone, since that changes neither number, and rules out emitting a proton, which would decrease the atomic number.
    3. An increase in atomic number with no change in mass number is exactly what happens in beta decay, where a neutron in the nucleus converts into a proton (increasing the atomic number by 1) and an electron, which is emitted, without changing the total number of nucleons.
    4. The answer is D.
    • Why not A: Alpha decay always reduces the mass number by 4 and the atomic number by 2, as an alpha particle (a helium nucleus) is emitted; here the mass number is unchanged and the atomic number has increased, which does not match alpha decay.
    • Why not B: Gamma emission alone involves only the release of energy as electromagnetic radiation, changing neither the mass number nor the atomic number; here the atomic number has increased by 1, which gamma emission alone cannot produce.
    • Why not C: If a proton were emitted directly from the nucleus, both the mass number and the atomic number would decrease by 1, since a proton has a mass number of 1 and carries one unit of positive charge; here the atomic number has increased, the opposite of what emitting a proton would cause.

13. Question 13Answer: A

    1. The three types of radiation differ greatly in how far they can penetrate matter: alpha particles are the least penetrating, beta particles penetrate further, and gamma radiation is the most penetrating.
    2. Alpha particles are stopped by just a sheet of paper or a few centimetres of air, because they interact strongly with matter and lose their energy quickly.
    3. Beta radiation needs a few millimetres of aluminium to be stopped, and gamma radiation needs a thick sheet of lead or a substantial thickness of concrete to be significantly reduced; paper does not stop either of these.
    4. So paper stops alpha radiation but not beta or gamma radiation, meaning the answer is A.
    • Why not B: A few millimetres of aluminium is thick enough to stop both alpha and beta radiation, so it does not fit a material that stops alpha but not beta; aluminium is the material typically used to stop the more penetrating beta radiation, well beyond what is needed to stop alpha.
    • Why not C: A thick sheet of lead stops alpha and beta radiation completely and greatly reduces gamma radiation as well, so it does not fit a material that stops alpha but leaves beta and gamma able to pass through; lead is used specifically because it is effective against the most penetrating type, gamma radiation.
    • Why not D: This confuses alpha's high ionising power with its penetrating power; alpha particles are in fact the least penetrating of the three types; because they interact so strongly with matter, they lose all their energy within a few centimetres of air or are stopped by a single sheet of paper.

14. Question 14Answer: C

    1. Background radiation comes from a mixture of natural sources, such as rocks and soil, cosmic rays from space, and food, as well as artificial (man-made) sources such as medical procedures and nuclear industry activity.
    2. Radon gas is a naturally occurring radioactive gas released from uranium-containing rocks and soil, and it makes up a significant fraction of natural background radiation.
    3. Hospital X-rays, weapons fallout and nuclear waste are all examples of artificial sources, produced by human activity rather than occurring naturally.
    4. The answer is C.
    • Why not A: Medical X-rays are a man-made (artificial) source of radiation exposure, deliberately produced by a machine for diagnostic imaging, rather than a naturally occurring source of background radiation.
    • Why not B: Fallout from nuclear weapons testing is an artificial source of radiation, produced by human activity, not a naturally occurring source that has always contributed to background radiation.
    • Why not D: Radioactive waste from a nuclear power station is an artificial, industrial source of radiation, produced as a byproduct of human activity, rather than a naturally occurring source.

15. Question 15Answer: B

    1. The number of half-lives that have passed is the total time divided by the half-life: 20 hours / 5 hours per half-life = 4 half-lives.
    2. Each half-life, the mass of undecayed nuclei halves: starting at 480 g, after 1 half-life it is 240 g, after 2 it is 120 g, after 3 it is 60 g, and after 4 it is 30 g.
    3. So after 20 hours (4 half-lives), the mass of undecayed nuclei has fallen to 30 g.
    4. The answer is B.
    • Why not A: This stops one half-life too early: 20 hours / 5 hours per half-life = 4 half-lives, so the mass must be halved four times (480 -> 240 -> 120 -> 60 -> 30), not three times (480 -> 240 -> 120 -> 60).
    • Why not C: This assumes that after a whole number of half-lives the sample has completely decayed to zero mass; in reality the mass halves repeatedly but never reaches exactly zero, no matter how many half-lives pass.
    • Why not D: This uses one half-life too many: 20 hours corresponds to 20 / 5 = 4 half-lives, not 5, so the mass should be halved four times (giving 30 g), not five times (which would give 15 g).