Radioactivity worksheet answers for GCSE physics (free PDF download)

Problem 1 Which radiation?

1. Alpha.
2. Beta.
3. Gamma.
4. Alpha: it ionises most strongly because it has a large mass and a +2 charge.

Problem 2 Inside a carbon-14 atom

1. The atomic number is the number of protons: 6.
2. Neutrons = mass number − atomic number = 14 − 6 = 8.
3. A neutral atom has equal numbers of protons and electrons: 6.
4. They have the same number of protons (6) but different numbers of neutrons (6 and 8).

Problem 3 Halving the activity

1. One half-life: 640 ÷ 2 = 320 Bq.
2. Two half-lives: 160 Bq.
3. 6.0 ÷ 2.0 = 3 half-lives: 640 → 320 → 160 → 80 Bq.

Problem 4 Units of radiation

1. 3.2 × 1000 = 3200 Bq.
2. 1.5 × 24 = 36 hours.
3. 0.5 × 1000 = 500 µSv.
4. 45 ÷ 60 = 0.75 hours.

Problem 5 Handling sources safely

1. Keep the time of exposure short, keep as far away as possible, point the source away from people, and never touch it or eat or drink nearby.
2. Lead absorbs the radiation, so the dose to people near the box is reduced.
3. Irradiation is exposure to radiation from an outside source. Contamination is when radioactive atoms get on or inside the body.

Problem 6 Subtracting the background

1. Any two: radon gas, rocks and soil, cosmic rays, food, medical scans.
2. Corrected rate = 58 − 12 = 46 counts per minute.
3. The detector also counts background radiation, so subtracting it gives only the counts from the source.

Problem 7 An alpha decay equation

1. 210 − 4 = 206.
2. 84 − 2 = 82.
3. Lead-206.

Problem 8 Beta decay equations

1. Mass number stays 24; atomic number 11 + 1 = 12, so the new nucleus is magnesium-24.
2. Mass number 131; atomic number 53 + 1 = 54.
3. A neutron changes into a proton and a fast electron (the beta particle) is emitted.

Problem 9 Half-life from a table

1. The rate falls from 800 to 400 in 20 minutes, so the half-life is 20 minutes (200 at 40 minutes agrees).
2. 60 ÷ 20 = 3 half-lives: 800 → 400 → 200 → 100 counts per minute.
3. 800 → 400 → 200 → 100 → 50 takes 4 half-lives: 4 × 20 = 80 minutes.

Problem 10 Reading a decay graph

1. The activity falls from 1600 Bq to 800 Bq at 8 days, so the half-life is 8 days.
2. 16 days is 2 half-lives: 1600 → 800 → 400 Bq.
3. At 12 days the graph reads about 570 Bq, between 800 Bq at 8 days and 400 Bq at 16 days (1600 × 0.5^1.5 = 566 Bq).
4. Each half-life removes only half of what is left, so some nuclei always remain and the activity gets smaller without reaching zero.

Problem 11 Which radiation does it emit?

1. Subtract 10: 400, 398, 130 and 2 counts per minute.
2. No alpha: paper does not change the count rate (400 to 398), and alpha would be stopped by paper.
3. Beta and gamma. Aluminium cuts the rate from 398 to 130, which shows beta is absorbed. The remaining 130 is absorbed by lead (2), which shows gamma.

Problem 12 Alpha inside and outside

1. Ionising radiation knocks electrons off atoms, producing ions.
2. Alpha travels only a few centimetres in air and cannot pass through the sealed case or the skin, so it is safe outside the body.
3. Inside the body all of the strongly ionising alpha energy is absorbed by nearby cells, causing serious damage.

Problem 13 Choosing an isotope

1. The gamma emitter with a 6-hour half-life: gamma passes out of the body to be detected, and the short half-life means it soon decays away.
2. The 430-year alpha emitter: alpha is stopped by the casing and the source lasts for decades.
3. A tracer should leave the patient’s body quickly with little dose, while a smoke detector must keep working for many years without replacement.

Problem 14 Balancing fission

1. Left: 1 + 235 = 236. Right: 141 + 92 + 3 = 236, so the mass numbers balance.
2. Left: 0 + 92 = 92. Right: 56 + 36 + 0 = 92, so the atomic numbers balance.
3. The neutrons released split other nuclei, which release more neutrons, so the reaction keeps itself going and speeds up.
4. Control rods absorb neutrons so the reaction rate stays steady.

Problem 15 Fission or fusion?

1. Fission: large nuclei such as uranium-235. Fusion: light nuclei such as hydrogen isotopes.
2. Fission is used in nuclear power stations. Fusion occurs in the Sun and other stars.
3. The nuclei are positively charged and repel one another, so they need very high speed (very high temperature) to get close enough to join.

Problem 16 A hospital dose

1. 09:00 to 03:00 is 18 h = 3 half-lives. 600 → 300 → 150 → 75 MBq.
2. 600 ÷ 2ⁿ below 10: n = 5 gives 18.75, n = 6 gives 9.375 MBq, so 6 half-lives.
3. 6 × 6.0 = 36 hours after 09:00, which is 21:00 on the next day.
4. The activity (and so the dose to the patient) falls quickly after the scan, with little long-term radiation.

Problem 17 Dating an old wooden bowl

1. 3.75 ÷ 15.0 = 1/4 (0.25).
2. 1/4 = (1/2)², so 2 half-lives.
3. 2 × 5730 = 11 460 years.
4. 7.5 ÷ 15.0 = 1/2, so 1 half-life: 5730 years.
5. Decay is random so counts fluctuate, and the original ratio in the living wood may have changed over time.

Problem 18 Spot the errors

1. After two half-lives one quarter remains; the activity falls by half each time but never reaches exactly zero.
2. In alpha decay the atomic number goes down by 2, and the mass number by 4.
3. Gamma rays only pass through the food; they do not make it radioactive. This is irradiation, not contamination, so the food is not radioactive afterwards.

Problem 19 Radiographer’s dose

1. 4.0 × 1800 = 7200 µSv = 7.2 mSv.
2. 7.2 ÷ 20 × 100 = 36 % of the limit.
3. 20 mm = 4 layers of 5 mm: 4.0 → 2.0 → 1.0 → 0.50 → 0.25 µSv per hour.
4. 0.25 × 1800 = 450 µSv.
5. Spend less time near the source and stand further away; wear a dosimeter badge to monitor the dose.

Problem 20 Mass turned into energy

1. E = m c² = 1.0 × 10⁻³ × (3.0 × 10⁸)² = 1.0 × 10⁻³ × 9.0 × 10¹⁶ = 9.0 × 10¹³ J.
2. t = E ÷ P = 9.0 × 10¹³ ÷ 1.0 × 10⁹ = 9.0 × 10⁴ s.
3. 90 000 ÷ 3600 = 25 hours.
4. Because c² is enormous, a tiny loss of mass releases a huge amount of energy, so the fuel’s mass hardly changes.