Radioactive decay
| English | Chinese | Pinyin |
|---|---|---|
| random | 随机 | suí jī |
| spontaneous | 自发 | zì fā |
| Geiger counter | 盖革计数器 | gài gé jì shù qì |
| activity | 活度 | huó dù |
| decay constant | 衰变常数 | shuāi biàn cháng shù |
| becquerel | 贝克勒尔 | bèi kè lēi ěr |
| half-life | 半衰期 | bàn shuāi qī |
Random 随机, yet predictable
- You can never say when a single nucleus will decay — it is random.
- Yet a huge sample of them decays in a smooth, predictable curve.
- Probability turns chaos into a reliable law.
Random and spontaneous 自发
- Decay is spontaneous — no trigger; unaffected by temperature, pressure or chemistry.
- It is random — a Geiger counter 盖革计数器 clicks at uneven intervals, never a steady stream.
Beta particles from a source leave thin, wispy tracks in a cloud chamber -- each track is one separate, random decay
Decay equations (α, β, γ)
Choose a decay type; the daughter nuclide is fixed so the nucleon number A and the proton number Z both balance.
Half-life — watch the nuclei decay
Each nucleus has a fixed chance of decaying, at random. Move time forward: about half the remaining nuclei decay every half-life — so the count halves, then halves again.
Select all the true statements about radioactive decay.
It is spontaneous and random, and the rate does not depend on conditions. You can only give the probability of a single decay.
Activity 活度 and decay constant 衰变常数
- Activity $A = \lambda N$ — decays per second (unit: becquerel 贝克勒尔, Bq).
- $\lambda$ is the decay constant — the probability per second that a nucleus decays.
The number of undecayed nuclei falls by half in each half-life 半衰期
The activity of a radioactive source is:
Activity = decay constant × number of undecayed nuclei, measured in becquerel.
A source has $\lambda = 0.010$ per second and $1.0 \times 10^{6}$ undecayed nuclei. What is its activity?
$A = \lambda N = 0.010 \times 1.0 \times 10^{6} = 1.0 \times 10^{4}\ \text{Bq}$.
Exponential decay
- The same fraction decays each second, so $N = N_0 e^{-\lambda t}$ (and $A = A_0 e^{-\lambda t}$).
- A $\ln$ plot is a straight line of gradient $-\lambda$.
The activity of a radioactive source decays exponentially with time.
The same fraction decays each second, giving $A = A_0 e^{-\lambda t}$.
Half-life
- The half-life $t_{1/2}$ is the time to fall to half: $t_{1/2} = \dfrac{\ln 2}{\lambda}$.
- After $n$ half-lives, a fraction $\left(\tfrac{1}{2}\right)^{n}$ remains.
The half-life is related to the decay constant by:
Setting $N = \tfrac{1}{2}N_0$ in $N = N_0 e^{-\lambda t}$ gives $\lambda t_{1/2} = \ln 2$.
What fraction of the nuclei remain after 3 half-lives?
Each half-life halves the number: $\left(\tfrac{1}{2}\right)^{3} = \tfrac{1}{8} = 0.125$.
You've got it
- decay is spontaneous and random (rate fixed, timing unpredictable)
- activity $A = \lambda N$ (Bq); $N = N_0 e^{-\lambda t}$
- half-life $t_{1/2} = \dfrac{\ln 2}{\lambda}$