The short answer
Alpha, beta and gamma decay, and the fixed-rate maths of half-life.
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Try the reasoning style
We treat forgetting as a failure — a lapse to be patched with reminders and records. Yet a mind that kept everything could not think; it would drown in the undifferentiated noise of every moment it had ever lived. To forget is not so much to lose information as to decide, mostly without our noticing, what was never worth keeping.
The author's argument relies most directly on which unstated assumption?
Pick an option to see how the tutor reasons to the answer — not just whether you were right.
Not quite — the answer is B.
Work backwards from the conclusion: a mind that ‘kept everything’ supposedly ‘could not think.’ That only follows if thinking means leaving most of experience out — so B is the premise the argument quietly rests on. A raises reliability, which the passage never weighs; C contradicts ‘mostly without our noticing’; D smuggles in a claim about intellect the passage never makes. The question rewards finding the hidden premise, not recalling a fact.
Unstable nuclei decay at a fixed, predictable rate. The key number is the half-life — the time for half of the nuclei present to decay. It's constant: each half-life, half of whatever remains decays, regardless of how much you started with.
The three decays
Alpha (α) & Beta (β)
- α: emits a helium nucleus (2p + 2n) → mass −4, atomic number −2
- β⁻: a neutron becomes a proton + emitted electron → atomic number +1, mass number unchanged
- Both change the element (the proton number changes)
Gamma (γ)
- Emits high-energy electromagnetic radiation
- No change to mass or atomic number
- Just sheds excess energy from the nucleus
The half-life rule
After half-lives, the fraction of the original sample remaining is . So after 1 half-life, remains; after 2, ; after 3, — and so on.
Worked example
A radioactive isotope has a half-life of 5 years. You start with 80 g. How much remains after 15 years?
Check yourself
After how many half-lives has a radioactive sample decayed to 1/16 of its original amount?
A real sample is rarely one pure nuclide, and the paper knows it. It prints a decay record and asks you to pull the two components apart. Below is that shape.
Passage· 3 questions on it
The following is adapted from a laboratory record. The sample is not one you are expected to have met.
| Time (h) | Count rate (counts per second) |
|---|---|
| 0 | 960 |
| 2 | 547 |
| 4 | 335 |
| 6 | 223 |
| 8 | 163 |
| 12 | 108 |
| 16 | 83 |
| 24 | 57 |
| 32 | 40 |
| 48 | 20 |
Q1 of 3 on this passage
The count rate falls by 43 per cent in the first two hours, but takes sixteen hours to fall by half between the 32-hour and 48-hour readings. What best explains the change of pace?
Q2 of 3 on this passage
What is the half-life of the longer-lived nuclide?
Q3 of 3 on this passage
Extrapolating the late readings back to time zero gives 160 counts per second for the longer-lived nuclide alone. What is the half-life of the shorter-lived nuclide?
Key takeaways
- Half-life = time for half the nuclei to decay; it's constant.
- After n half-lives, the fraction left is (1/2)ⁿ.
- Alpha: emits a He nucleus (mass −4, atomic number −2).
- Beta⁻: a neutron → proton + emitted electron (atomic number +1).
- Gamma: energy only — no change to mass or atomic number.
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