GCSE Physics - Radioactivity

For isotope X:

• 4 half-lives have passed in 8 days (1 mark)
• 800 → 400 → 200 → 100 → 50 atoms of X remain (1 mark)

For isotope Y:

• 2 half-lives have passed in 8 days (1 mark)
• 800 → 400 → 200 atoms of Y remain
• Final ratio X:Y = 50:200 = 1:4 (1 mark)

• Normal true count rate = 300 - 20 = 280 cpm (1 mark)
• Count rate with smoke = 30 - 20 = 10 cpm (1 mark)
• Percentage reduction = (270/280) × 100 = 96.4% (1 mark)

Accept answers between 96% and 96.5%

• Initial true count = 920 cpm (1 mark)
• Final true count = 75 cpm
• 920 → 460 → 230 → 115 requires 3 half-lives (1 mark)
• Time = 3 × 20 = 60 minutes (1 mark)

Method showing:

• α decay: -4, -2 for mass and atomic numbers
• β decay: 0, +1 for mass and atomic numbers
• Overall mass number change = -8 (2 × -4) (1 mark)
• Overall atomic number change = -2 ((-2) + 1 + (-2) + 1) (2 marks)

• Each 5cm halves the intensity twice (1 mark)
• To reach 1/16, need to halve intensity 4 times (1 mark)
• Therefore need 10cm of lead (1 mark)

Accept clear reasoning showing exponential decrease

• Using inverse square law: I₁r₁² = I₂r₂² (1 mark)
• r = 2√(240/50) = 4.38m (1 mark)

Accept 4.4m or any answer between 4.3m and 4.4m

• Slower neutrons spend more time near nucleus (1 mark)
• Nuclear forces have very short range (1 mark)
• Therefore increased chance of interaction/capture (1 mark)

• 3.5 half-lives means 3 complete half-lives plus half of another (1 mark)
• 4000 → 2000 → 1000 → 500 → 354 Bq (1 mark)

Accept answers between 350 and 355 Bq

Because of background radiation always being present (1 mark)

Accept reference to natural radiation sources

The electron is created when a neutron changes into a proton (1 mark)

Accept reference to nuclear transformation