Radioactive decay (A-level only) Flashcards – AQA A-level Physics (7408)

What does it mean that radioactive decay is random for an individual unstable nucleus?

It is impossible to predict when the nucleus will decay.

What does the decay constant $\lambda$ represent, and what are its units?

The constant decay probability per unit time for an undecayed nucleus of a given nuclide. Its units are inverse time.

Does an unstable nucleus's decay probability per unit time depend on its age?

No; it is independent of the nucleus's age.

What is the approximate probability that an undecayed nucleus decays during a sufficiently short interval $\Delta t$?

$\lambda\Delta t$

What equation describes the expected rate of change of the number $N$ of undecayed nuclei in a large population?

$\frac{dN}{dt}=-\lambda N$ Over a sufficiently short interval: $\frac{\Delta N}{\Delta t}=-\lambda N$.

What exponential law gives the expected number of undecayed nuclei at time $t$?

$N=N_0\mathrm{e}^{-\lambda t}$, where $N_0$ is the initial number of nuclei.

How does the exponential decay law relate to random fluctuations?

It describes expected population behaviour; individual decays and small populations show random fluctuations.

How can a constant-probability model simulate radioactive decay?

Give each surviving nucleus the same chance of decay in each equal time interval, remove those that decay, and repeat.

How can the number of nuclei of a nuclide be calculated from its mass and molar mass?

$N=\frac{m}{M}N_{\mathrm A}$, where $m$ is the mass of the nuclide and $M$ is its molar mass.

What is radioactive activity?

The number of nuclear decays per unit time.

What is the SI unit of activity, and what does one unit represent?

The becquerel ($\mathrm{Bq}$); one becquerel is one decay per second.

How is activity $A$ related to the number of undecayed nuclei $N$ and the decay constant $\lambda$?

$A = \lambda N$

How is activity $A$ related to the rate of change of the number of undecayed nuclei $N$?

$A = -\frac{dN}{dt}$

What equation gives activity $A$ at time $t$ in terms of initial activity $A_0$ and decay constant $\lambda$?

$A = A_0\mathrm{e}^{-\lambda t}$

What does radioactive dating estimate, and what property of the nuclide must be known?

It estimates elapsed time from radioactive decay, using a known decay constant or half-life.

What exponential decay law relates the remaining quantity or activity to its initial value?

$Q = Q_0 e^{-\lambda t}$ Here $Q$ is the quantity or activity at time $t$, $Q_0$ is its initial value, and $\lambda$ is the decay constant.

What must be established or inferred to calculate elapsed time from a remaining quantity or activity?

Its initial value.

What two assumptions about the dated material affect the reliability of radioactive dating?

Assumptions about its initial composition and whether radioactive material has been gained or lost since the time being dated.

How should a nuclide’s half-life relate to the timescale being investigated in radioactive dating?

It must be suitable for the timescale being investigated.

For how long must radioactive waste be managed?

For as long as its radiation presents an unacceptable hazard.

Why does the activity of radioactive waste decrease over time?

Its radioactive nuclei decay.

How does half-life help indicate changes in activity over storage timescales?

A shorter-lived nuclide’s activity falls more rapidly; a long-lived nuclide can remain radioactive for a long time.

Besides half-life, what three factors matter when assessing radioactive waste hazards and storage needs?

The activity, the radiation emitted, and the potential for material to escape or be encountered.

What must radioactive waste storage achieve for an appropriate period?

Contain the material and limit exposure.