Senior 6 practice book · Unit 5 of 10

Atomic Nuclei and Radioactive Decay

50 questions that complete the Senior 6 quiz for this unit: 27 core and 23 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

After two half-lives a radioactive sample has completely decayed.Each half-life halves what is left: after two half-lives a quarter remains, after three an eighth, and so on; it never quite reaches zero.
A nucleus with a bigger total binding energy must be more stable.Stability is judged by binding energy PER NUCLEON; uranium has a huge total binding energy but less per nucleon than iron, so it is less tightly bound.
Food or equipment exposed to gamma rays becomes radioactive.Gamma irradiation kills microbes but does not make the object radioactive, because it does not change the nuclei of the object's atoms.
Alpha particles are the most dangerous radiation in every situation.Outside the body alpha is stopped by the dead outer layer of skin; it is most dangerous when swallowed or breathed in, while gamma is the main hazard from a source outside the body.
The strong nuclear force holds the whole atom together.The strong force acts only between nucleons over about 10⁻¹⁵ m, holding the nucleus together; electrons are held to the nucleus by the electric force.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Structure of the nucleus: nucleons, A and Z, nuclide notation, isotopes
Size and density of nuclei (r = r₀A^1/3)
Nuclear forces and stability: strong force, N–Z stability curve
Alpha, beta (β⁻, β⁺) and gamma decay; balancing decay equations
Properties of α, β and γ: ionisation, penetration, deflection in fields
Detecting radiation: GM tube, cloud chamber, background radiation
Half-life and the random nature of decay
Decay law, decay constant and activity (A = λN, N = N₀e^−λt)
Mass defect, binding energy and binding energy per nucleon; energy released in reactions
Nuclear fission, chain reactions and reactors
Nuclear fusion and the energy of stars
Uses of radioisotopes in medicine, industry and agriculture (tracers, gauges, sterilising)
Biological effects of ionising radiation and safe handling of sources

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 23 harder ones are marked ★ Challenge.

1True or false
The Sun's energy comes from the fission of heavy elements in its core.
Show answer
Answer: False
The Sun is powered by fusion, mainly of hydrogen into helium.
Common mistakeConfusing fission with fusion: stars join light nuclei together; they are not powered by splitting heavy ones.
2Multiple choice · ★ Challenge
Hospitals sterilise sealed packs of syringes with gamma rays from cobalt-60. What is the main advantage of this method?
1. AIt makes the syringes slightly radioactive, which goes on killing germs later
2. BIt can sterilise items already sealed in their packets, without heating them
3. CGamma rays are stopped by the packet, so the syringes inside are safe to use
4. DIt works faster than any other method because gamma rays are slow
Show answer
Answer: B. It can sterilise items already sealed in their packets, without heating them
Penetrating gamma rays kill microbes right through the sealed packaging, and no heat is needed, so plastic items are not damaged; the items do not become radioactive.
Common mistakeChoosing 'makes the syringes radioactive' is the classic misconception: irradiation does not make objects radioactive.
3True or false
All nuclei have roughly the same density, whatever their nucleon number.
Show answer
Answer: True
Volume ∝ r³ ∝ A and mass ∝ A, so the density (mass ÷ volume) is about the same for every nucleus.
Common mistakeThinking heavy nuclei are denser forgets that their volume grows in proportion to the number of nucleons.
4Multiple choice · ★ Challenge
Carbon-11 (Z = 6), used in PET scans, decays by β⁺ emission. Which equation is correct?
1. A¹¹₆C → ¹¹₇N + ⁰₋₁e + ν̄
2. B¹¹₆C → ¹¹₅B + ⁰₊₁e + ν
3. C¹¹₆C → ⁷₄Be + ⁴₂He
4. D¹¹₆C → ¹¹₅B + ⁰₋₁e + ν
Show answer
Answer: B. ¹¹₆C → ¹¹₅B + ⁰₊₁e + ν
In β⁺ decay a proton becomes a neutron: Z falls by 1 (6 → 5, boron), A is unchanged, and a positron and a neutrino are emitted.
Common mistakeThe first equation is β⁻ decay; for β⁺ the emitted particle is a positron (charge +1) and Z decreases.
5True or false
Gamma rays are deflected by an electric field because they carry energy.
Show answer
Answer: False
Gamma rays are photons with no charge, so electric and magnetic fields do not deflect them.
Common mistakeLinking energy with deflection is wrong: only charged particles feel a force in an electric field.
6Multiple choice · ★ Challenge
Why do alpha particles produce far more ions per centimetre of air than beta particles?
1. AThey travel faster than beta particles, so they hit more atoms every second
2. BThey are uncharged, so they can get close to the electrons
3. CThey carry a double charge and move slowly, so they act strongly on each atom
4. DThey are electromagnetic waves
Show answer
Answer: C. They carry a double charge and move slowly, so they act strongly on each atom
The +2e charge and low speed mean strong, long-lasting electric forces on nearby electrons, so many ions are formed and the α energy is used up in a few cm.
Common mistakeChoosing 'they travel faster' gets it backwards: slow particles spend longer near each atom and ionise more.
7True or false
The strong nuclear force acts between nucleons that are many metres apart.
Show answer
Answer: False
It has a very short range, about 10⁻¹⁵ m (a few nucleon diameters); beyond that it is negligible.
Common mistakeThinking the strong force has long range like gravity forgets that it only acts inside the nucleus.
8Fill in the blank · ★ Challenge
In N = N₀e^−λt, the time 1/λ, after which the number of nuclei has fallen to 1/e of its starting value, is called the mean ______.
Show answer
Answer: life
Mean life τ = 1/λ = T½/0.693 ≈ 1.44 T½.
Common mistakeWriting 'half-life' is wrong: in one half-life N falls to ½, but in 1/λ it falls further, to 1/e ≈ 0.37.
9True or false
A patient who has been treated with a beam of gamma rays becomes radioactive.
Show answer
Answer: False
The gamma rays ionise atoms in the tissue but do not change the nuclei, so the patient does not become a source of radiation.
Common mistakeConfusing irradiation (being exposed to radiation) with contamination (having radioactive material on or in the body).
10True or false
A nucleus with a larger total binding energy is always more stable than one with a smaller total binding energy.
Show answer
Answer: False
Stability depends on binding energy per nucleon; uranium-235 has a much larger total than iron-56 but less per nucleon.
Common mistakeComparing totals favours big nuclei simply because they have more nucleons.
11Multiple choice · ★ Challenge
Why do stable heavy nuclei, such as lead-208, contain many more neutrons than protons?
1. ANeutrons are lighter than protons, so they fit more easily
2. BProtons decay into neutrons in heavy nuclei until the forces balance exactly
3. CNeutrons add strong-force attraction without adding electric repulsion
4. DExtra neutrons cancel the charge of the protons
Show answer
Answer: C. Neutrons add strong-force attraction without adding electric repulsion
The electric repulsion between protons acts across the whole nucleus and grows quickly with Z; extra neutrons add binding (strong force) with no repulsion.
Common mistakeChoosing 'cancel the charge' is wrong: neutrons are uncharged and cannot cancel anything; they help by adding attraction.
12True or false
The products of the fission of uranium-235 are usually themselves radioactive.
Show answer
Answer: True
The fragments have too many neutrons for their size, so they decay by β⁻ emission; this is why spent fuel is dangerous waste.
Common mistakeThinking fission makes uranium 'safe' ignores that the fission fragments are strongly radioactive, often for many years.
13Multiple choice · ★ Challenge
By what factor is the radius of a nucleus with A = 216 larger than that of a nucleus with A = 27?
1. A8
2. B2.8
3. C4
4. D2
Show answer
Answer: D. 2
r ∝ A^1/3: (216 ÷ 27)^1/3 = 8^1/3 = 2.
Common mistake8 is the ratio of the nucleon numbers (and of the volumes); the radius grows only as the cube root.
14Fill in the blank
Nuclei that have the same nucleon number but different proton numbers, such as ¹⁴₆C and ¹⁴₇N, are called ______.
Show answer
Answer: isobars
Same A, different Z: isobars. Same Z, different A: isotopes.
Common mistakeWriting 'isotopes' is wrong here: isotopes have the same proton number, but carbon and nitrogen are different elements.
15Multiple choice · ★ Challenge
A worker standing 0.50 m from a small gamma source steps back so that she is 1.5 m from it. By what factor does the dose rate she receives fall (inverse-square law)?
1. A3
2. B1.5
3. C27
4. D9
Show answer
Answer: D. 9
Dose rate ∝ 1/r²; the distance is 3 times larger, so the dose rate falls by 3² = 9.
Common mistake3 forgets to square the distance ratio; gamma intensity from a point source falls as 1/r².
16Fill in the blank
When a nucleus emits a β⁻ particle, its proton number increases by ______ and its nucleon number stays the same.
Show answer
Answer: 1
A neutron turns into a proton (and an electron is emitted), so Z rises by 1 while A is unchanged.
Common mistakeWriting 'decreases' confuses β⁻ with β⁺ or α; in β⁻ decay the nucleus gains a proton.
17Multiple choice · ★ Challenge
Two sources start with equal activities. Source P has a half-life of 2.0 h and source Q a half-life of 6.0 h. What is the ratio of their activities, P : Q, after 6.0 h?
1. A1 : 3
2. B1 : 4
3. C3 : 1
4. D1 : 8
Show answer
Answer: B. 1 : 4
After 6.0 h, P has gone through 3 half-lives (1/8 left) and Q through 1 (1/2 left): ratio = (1/8) : (1/2) = 1 : 4.
Common mistake1 : 3 compares the half-lives directly; the activities fall by powers of ½, not in proportion to time.
18Fill in the blank
The ionising radiation always present around us, from rocks, radon gas, cosmic rays and food, is called ______ radiation.
Show answer
Answer: background
Background radiation must be measured and subtracted from count rates in experiments.
Common mistakeWriting 'cosmic' names only one source; the total from all natural and man-made sources is the background.
19Short answer · ★ Challenge
Explain why an alpha source is fairly harmless outside the body but very dangerous if it is swallowed or breathed in.
Show answer
Model answer: Alpha particles are stopped by a few cm of air or by the dead outer layer of the skin, so from outside they do not reach living cells. Inside the body the source sits next to living tissue, and the strongly ionising alpha particles deposit all their energy in a tiny region, causing severe damage to cells and DNA.
Common mistakeSaying alpha is always the least dangerous because it is the least penetrating ignores where the source is; low penetration means high ionisation where it stops.
20True or false
If a sample contains exactly 1000 radioactive nuclei, exactly 500 will remain after one half-life.
Show answer
Answer: False
Decay is random; half-life is a statistical average, so about 500 remain, but the actual number varies, especially for small samples.
Common mistakeTreating half-life as an exact rule for each sample ignores the random nature of decay.
21Multiple choice
Protons in a nucleus repel one another. What holds the nucleus together?
1. AGravity between the nucleons, which is large inside such a tiny space
2. BThe strong nuclear force, a short-range attraction between all nucleons
3. CThe electrons orbiting the nucleus
4. DMagnetic attraction between protons
Show answer
Answer: B. The strong nuclear force, a short-range attraction between all nucleons
The strong force is attractive between protons and neutrons alike and, at distances of about 10⁻¹⁵ m, is far stronger than the electric repulsion.
Common mistakeChoosing gravity is wrong: between nucleons it is about 10³⁶ times weaker than the electric repulsion, far too weak to hold them.
22Short answer · ★ Challenge
Explain why the activity of a sample halves in the same time as the number of undecayed nuclei halves.
Show answer
Model answer: The activity is A = λN, where λ is a constant for the isotope. A is therefore proportional to N, so when N halves A also halves, in the same half-life.
Common mistakeThinking the activity falls faster than N assumes λ changes with time; λ is fixed for a given isotope.
23Multiple choice · ★ Challenge
The radius of a nucleus is r = r₀A^1/3 with r₀ = 1.2 fm. What is the radius of a nucleus with A = 125?
1. A6.0 fm
2. B150 fm
3. C13 fm
4. D1.2 fm
Show answer
Answer: A. 6.0 fm
125^1/3 = 5, so r = 1.2 × 5 = 6.0 fm (6.0 × 10⁻¹⁵ m).
Common mistake150 fm multiplies by A itself; 13 fm uses the square root instead of the cube root.
24Multiple choice
Which properties make an isotope suitable as a medical tracer injected into a patient?
1. AAlpha emitter with a half-life of many years
2. BBeta emitter with a half-life of a few seconds
3. CGamma emitter with a half-life of a few hours
4. DGamma emitter with a half-life of thousands of years
Show answer
Answer: C. Gamma emitter with a half-life of a few hours
Gamma rays pass out of the body to the camera and ionise little; a half-life of hours is long enough for the scan but gives a small total dose.
Common mistakeChoosing a long half-life ignores the patient: the source would keep irradiating the body for years after the scan.
25Fill in the blank
A household smoke alarm contains a weak americium-241 source that emits ______ particles, which ionise the air between two plates.
Show answer
Answer: alpha
The strongly ionising alpha particles allow a small current; smoke absorbs them, the current falls and the alarm sounds.
Common mistakeWriting 'gamma' is wrong: gamma ionises too weakly to give a measurable current across the small air gap.
26Short answer · ★ Challenge
Explain why a small lump of uranium-235 does not sustain a chain reaction, while a larger lump above the critical mass does.
Show answer
Model answer: Each fission releases 2–3 neutrons. In a small lump a large share of the neutrons escape through the surface before they can cause another fission, so on average less than one new fission follows each one and the reaction dies out. In a larger lump the volume (where fissions happen) grows faster than the surface area (where neutrons escape), so at the critical mass at least one neutron per fission causes another and the chain reaction keeps going.
Common mistakeSaying small lumps 'do not have enough energy' misses the mechanism: the issue is neutron loss through the surface.
27Multiple choice
Which of these is NOT a source of the natural background radiation measured in a school laboratory in Rwanda?
1. ARadon gas seeping out of granite rocks
2. BCosmic rays arriving from space
3. CPotassium-40 in beans and bananas
4. DRadio waves from phone masts
Show answer
Answer: D. Radio waves from phone masts
Radio waves are non-ionising electromagnetic waves; background radiation is ionising radiation from rocks, radon, cosmic rays, food and medical uses.
Common mistakeChoosing potassium-40 is wrong: the body naturally contains radioactive K-40 from foods such as bananas and beans.
28Multiple choice · ★ Challenge
A GM counter records 260 counts in 2.0 minutes near a source. The background count rate is 30 counts per minute. What is the count rate due to the source?
1. A100 counts/min
2. B230 counts/min
3. C115 counts/min
4. D130 counts/min
Show answer
Answer: A. 100 counts/min
Measured rate = 260 ÷ 2.0 = 130 counts/min; corrected rate = 130 − 30 = 100 counts/min.
Common mistake230 subtracts the background rate from the 2-minute total; first turn the total into a rate per minute.
29Multiple choice
A technician must move a sealed gamma source from its store to an experiment. Which way of working gives her the smallest exposure?
1. ACarry it in her hand, but walk as quickly as she can
2. BWear a thick cotton laboratory coat and carry it in her pocket
3. CUse long tongs, hold it at arm's length and keep the task short
4. DWear rubber gloves and hold it close to her body to keep it steady
Show answer
Answer: C. Use long tongs, hold it at arm's length and keep the task short
Exposure is reduced by distance (dose rate falls roughly as 1/r²), short time and shielding; long tongs add distance.
Common mistakeChoosing the lab coat is wrong: cloth is no shield for gamma rays; distance and time are what reduce the dose.
30Multiple choice · ★ Challenge
Total binding energies: helium-4, 28.3 MeV; iron-56, 492 MeV; uranium-235, 1784 MeV. Which nucleus is most tightly bound, and why?
1. AIron-56, because it has the largest binding energy per nucleon (about 8.8 MeV)
2. BUranium-235, because it has the largest total binding energy
3. CHelium-4, because it has the fewest nucleons and so the least to hold together
4. DAll are equally stable, since all three are found in nature on Earth
Show answer
Answer: A. Iron-56, because it has the largest binding energy per nucleon (about 8.8 MeV)
Per nucleon: He 28.3 ÷ 4 ≈ 7.1 MeV; Fe 492 ÷ 56 ≈ 8.8 MeV; U 1784 ÷ 235 ≈ 7.6 MeV. Iron has the most per nucleon.
Common mistakeChoosing uranium uses the total binding energy, which is large just because it has many nucleons; stability depends on the energy per nucleon.
31Multiple choice
Why does nuclear fusion need extremely high temperatures, such as those in the core of the Sun?
1. ATo melt the hydrogen so that its nuclei can flow together
2. BTo give nuclei enough energy to overcome their electric repulsion
3. CTo produce the neutrons that start the fusion chain reaction
4. DTo split the nuclei first
Show answer
Answer: B. To give nuclei enough energy to overcome their electric repulsion
Nuclei are positively charged and repel; only at temperatures of about 10⁷ K are they fast enough to come within range of the strong force.
Common mistakeChoosing 'to split the nuclei first' confuses fusion with fission; fusion joins light nuclei together.
32Multiple choice · ★ Challenge
A sample of 3.0 × 10¹² nuclei has an activity of 1.5 × 10⁸ Bq. What is the half-life?
1. A5.6 h
2. B0.39 h
3. C231 h
4. D3.9 h
Show answer
Answer: D. 3.9 h
λ = A/N = 1.5 × 10⁸ ÷ 3.0 × 10¹² = 5.0 × 10⁻⁵ s⁻¹; T½ = 0.693 ÷ λ = 13 860 s ≈ 3.9 h.
Common mistake5.6 h is 1/λ (the mean life), which forgets the factor ln 2 = 0.693.
33Short answer
State three precautions that a teacher should take when using a radioactive source in a school laboratory.
Show answer
Model answer: Handle the source with long tongs, never with the fingers, and hold it at arm's length pointing away from people; keep it out of its lead-lined box for the shortest possible time; store it locked in the box, labelled; do not eat or drink in the lab and wash hands afterwards.
Common mistakeSaying 'wear sunglasses' or 'open the windows' does not protect against ionising radiation; distance, time and shielding are the key ideas.
34Short answer · ★ Challenge
On a chart of neutron number N against proton number Z, stable nuclei lie along a band. State the type of decay expected for a nucleus lying (a) above the band (too many neutrons), (b) below the band (too many protons), (c) beyond Z = 83. Explain (a).
Show answer
Model answer: (a) β⁻ decay; (b) β⁺ decay (or electron capture); (c) usually α decay. In (a) a neutron changes into a proton (n → p + e⁻ + ν̄), so N falls by 1 and Z rises by 1, moving the nucleus towards the stable band.
Common mistakeChoosing β⁺ for a neutron-rich nucleus moves it the wrong way: β⁺ turns a proton into a neutron, adding to the excess.
35Multiple choice
A beam containing α, β⁻ and γ radiation passes through a magnetic field at right angles to it. What happens?
1. Aα and β⁻ bend in opposite directions, β⁻ more sharply; γ goes straight on
2. BAll three bend the same way, γ least because it has no mass
3. COnly γ is deflected
4. Dα and β⁻ bend the same way, with α bending more sharply than β⁻
Show answer
Answer: A. α and β⁻ bend in opposite directions, β⁻ more sharply; γ goes straight on
Opposite charges are pushed opposite ways; the light β⁻ particle is deflected far more than the heavy α; γ is uncharged.
Common mistakeChoosing 'α bends more sharply' forgets that α particles are about 7000 times heavier than electrons, so they are hard to deflect.
36Short answer · ★ Challenge
A nucleus X emits one alpha particle and then two β⁻ particles. Show that the final nucleus is an isotope of X, and state how its nucleon number has changed.
Show answer
Model answer: Alpha: A − 4, Z − 2. Each β⁻: A unchanged, Z + 1, so two give Z + 2. Final: nucleon number A − 4, proton number Z − 2 + 2 = Z. Same Z means the same element, so it is an isotope of X with 4 fewer nucleons (4 fewer neutrons).
Common mistakeForgetting that β⁻ decay raises Z gives Z − 2, a different element; each β⁻ adds one proton.
37Multiple choice
What fraction of the original radioactive nuclei in a sample has DECAYED after three half-lives?
1. A7/8
2. B3/8
3. C1/8
4. D1/3
Show answer
Answer: A. 7/8
Remaining = (½)³ = 1/8, so decayed = 1 − 1/8 = 7/8.
Common mistake1/8 is the fraction REMAINING; the question asks how much has decayed.
38Multiple choice
Caesium-137, ¹³⁷₅₅Cs, is a fission product found in spent reactor fuel. What is the neutron number of this nuclide?
1. A82
2. B55
3. C137
4. D192
Show answer
Answer: A. 82
Neutrons N = A − Z = 137 − 55 = 82.
Common mistake137 is the total number of nucleons; 192 adds A and Z instead of subtracting.
39Short answer · ★ Challenge
Engineers suspect a leak in a water pipe buried 1 m under a road in Kigali. Explain how a radioactive tracer could find the leak and what kind of isotope they should choose.
Show answer
Model answer: Add a small amount of tracer to the water and move a detector along the ground above the pipe; where the water leaks, the tracer collects in the soil and the count rate rises. The isotope should be a gamma emitter (to pass through 1 m of soil) with a short half-life of hours or days, so it is active during the test but soon becomes harmless; it should also be soluble and not harmful in the low amount used.
Common mistakeChoosing an alpha emitter would fail: its radiation cannot pass through the pipe and soil to reach the detector.
40Multiple choice
Polonium-210 (Z = 84) decays by emitting an alpha particle. What is the daughter nucleus?
1. A²⁰⁶₈₂Pb
2. B²¹⁰₈₂Pb
3. C²⁰⁶₈₄Po
4. D²⁰⁸₈₃Bi
Show answer
Answer: A. ²⁰⁶₈₂Pb
Alpha emission removes ⁴₂He: A = 210 − 4 = 206, Z = 84 − 2 = 82, which is lead.
Common mistake²¹⁰₈₂Pb changes only Z; an alpha particle carries away 4 nucleons, so A must also fall by 4.
41Short answer · ★ Challenge
A class models decay with 600 dice: each throw, every die showing a six is removed. Explain what the dice model shows about radioactive decay and estimate the 'half-life' in throws.
Show answer
Model answer: Each die has a fixed chance (1/6) of being removed in each throw, but no one can predict which die will go, just as decay is random with a fixed probability λ per unit time. The number removed per throw is proportional to the number left, giving an exponential fall. (5/6)ⁿ = ½ gives n = ln 2 ÷ ln(6/5) ≈ 3.8 throws.
Common mistakeSaying 100 dice go every throw (600 ÷ 6) for six throws treats decay as linear; the number removed falls as fewer dice remain.
42Short answer
In a cloud chamber, alpha and beta particles leave different tracks. Describe the tracks and explain the difference.
Show answer
Model answer: Alpha tracks are short, thick and straight, and all about the same length. Beta tracks are thin, longer and twisted. Alpha particles ionise strongly (thick trail) and lose energy quickly (short range); being heavy they are not knocked off course. Light beta particles ionise weakly and are easily deflected by collisions with electrons.
Common mistakeSaying the thicker track means a bigger particle confuses size with ionisation: the thickness shows how many ions are made per cm.
43Multiple choice · ★ Challenge
A nuclear power station produces 1000 MW of electrical power at an efficiency of 33 %. Each fission releases 200 MeV (1 MeV = 1.6 × 10⁻¹³ J). About how many fissions occur each second?
1. A3.1 × 10¹⁹
2. B1.0 × 10¹⁹
3. C9.4 × 10¹⁹
4. D9.4 × 10²²
Show answer
Answer: C. 9.4 × 10¹⁹
Thermal power = 1000 MW ÷ 0.33 ≈ 3.0 × 10⁹ W; energy per fission = 200 × 1.6 × 10⁻¹³ = 3.2 × 10⁻¹¹ J; rate = 3.0 × 10⁹ ÷ 3.2 × 10⁻¹¹ ≈ 9.4 × 10¹⁹ s⁻¹.
Common mistake3.1 × 10¹⁹ ignores the efficiency: the reactor must produce about three times the electrical output as heat.
44Multiple choice
A sample contains 5.0 × 10¹⁰ undecayed nuclei with a decay constant of 2.0 × 10⁻⁴ s⁻¹. What is its activity?
1. A2.5 × 10¹⁴ Bq
2. B1.0 × 10⁷ Bq
3. C4.0 × 10⁻¹⁵ Bq
4. D3.5 × 10⁶ Bq
Show answer
Answer: B. 1.0 × 10⁷ Bq
A = λN = 2.0 × 10⁻⁴ × 5.0 × 10¹⁰ = 1.0 × 10⁷ Bq.
Common mistake2.5 × 10¹⁴ Bq divides N by λ; activity is the product λN.
45Short answer · ★ Challenge
A deuteron (²₁H) has mass 2.01355 u; a proton is 1.00728 u and a neutron 1.00867 u. Calculate its binding energy (1 u ↔ 931.5 MeV) and the minimum energy of a gamma photon that could split it.
Show answer
Model answer: Mass defect = 1.00728 + 1.00867 − 2.01355 = 0.00240 u. Binding energy = 0.00240 × 931.5 ≈ 2.24 MeV (1.12 MeV per nucleon). A photon needs at least 2.24 MeV to separate the proton and neutron.
Common mistakeSubtracting the masses the wrong way round gives a negative defect; the separate nucleons always have MORE mass than the nucleus.
46Multiple choice
What is the job of the moderator (graphite or water) in a thermal nuclear reactor?
1. ATo slow fast neutrons so that U-235 captures them more easily
2. BTo absorb neutrons and stop the reaction whenever it gets too fast
3. CTo carry heat to the turbines
4. DTo shield workers from gamma rays
Show answer
Answer: A. To slow fast neutrons so that U-235 captures them more easily
Neutrons from fission are fast; collisions with light moderator nuclei slow them to thermal speeds, at which U-235 is much more likely to undergo fission.
Common mistakeChoosing 'absorb neutrons' describes the control rods; the moderator slows neutrons without absorbing them.
47Multiple choice
A factory making plastic sheet controls its thickness by placing a source on one side and a detector on the other. Which source is best?
1. AAn alpha source
2. BA beta source
3. CA gamma source
4. DA source of neutrons
Show answer
Answer: B. A beta source
Beta is partly absorbed by thin plastic, so small changes in thickness change the count rate noticeably; alpha would be stopped completely and gamma would hardly be affected.
Common mistakeChoosing gamma is wrong: it passes almost unchanged through a thin sheet, so the detector cannot sense small thickness changes.
48Short answer · ★ Challenge
In the fusion reaction ²₁H + ²₁H → ³₂He + ¹₀n, the masses are: ²H = 2.01410 u, ³He = 3.01603 u, n = 1.00867 u. Calculate the energy released in MeV (1 u ↔ 931.5 MeV).
Show answer
Model answer: Mass before = 2 × 2.01410 = 4.02820 u. Mass after = 3.01603 + 1.00867 = 4.02470 u. Mass lost = 0.00350 u. Energy = 0.00350 × 931.5 ≈ 3.26 MeV.
Common mistakeUsing one deuterium mass instead of two on the left gives a negative answer; count every particle on each side.
49Multiple choice
Using E = mc², how much energy is equivalent to a mass of 1 u = 1.66 × 10⁻²⁷ kg? (c = 3.0 × 10⁸ m/s)
1. A5.0 × 10⁻¹⁹ J
2. B1.5 × 10⁻¹⁰ J
3. C931.5 J
4. D1.5 × 10⁻¹⁹ J
Show answer
Answer: B. 1.5 × 10⁻¹⁰ J
E = mc² = 1.66 × 10⁻²⁷ × (3.0 × 10⁸)² = 1.66 × 10⁻²⁷ × 9.0 × 10¹⁶ ≈ 1.5 × 10⁻¹⁰ J (= 931.5 MeV).
Common mistake5.0 × 10⁻¹⁹ J uses c instead of c²; 931.5 J mixes up MeV with joules.
50Short answer · ★ Challenge
Estimate the density of nuclear matter by treating one nucleon (mass 1.67 × 10⁻²⁷ kg) as a sphere of radius 1.2 × 10⁻¹⁵ m. Compare your answer with the density of water (1000 kg/m³) and comment.
Show answer
Model answer: Volume = (4/3)πr³ = (4/3)π(1.2 × 10⁻¹⁵)³ ≈ 7.2 × 10⁻⁴⁵ m³. Density = 1.67 × 10⁻²⁷ ÷ 7.2 × 10⁻⁴⁵ ≈ 2.3 × 10¹⁷ kg/m³, about 10¹⁴ times the density of water. Almost all the mass of an atom is packed into the tiny nucleus; the rest of the atom is mostly empty space.
Common mistakeUsing the radius of an atom (about 10⁻¹⁰ m) gives an ordinary density; the point is that the nucleus is about 10⁵ times smaller than the atom.