Quick questions on Half-life and decay explained: O-Level Physics

Radioactive decay is random: you cannot say when any one nucleus will decay. But in a large sample, a predictable fraction decays each second, so the behaviour of the whole sample is regular even though each nucleus is unpredictable.

The activity of a source is the number of nuclei that decay per second, measured in becquerels ($\text{Bq}$), where $1\ \text{Bq}$ is one decay per second. As the undecayed nuclei run out, the activity falls.

The half-life is the time taken for half of the undecayed nuclei in a sample to decay. Equivalently, it is the time for the activity to fall to half its value. Each isotope has its own characteristic half-life, ranging from fractions of a second to billions of years.

After each half-life, the number of undecayed nuclei (and the activity) halves:

A graph of activity (or undecayed nuclei) against time is a curve that falls steeply at first and then more gently, halving over each half-life and approaching, but never quite reaching, zero.

Define the half-life of a radioactive isotope. [2 marks]

A source of activity $640\ \text{Bq}$ has a half-life of $2$ hours. Find its activity after $6$ hours. [2 marks]

A sample has $4.8 \times 10^{6}$ undecayed nuclei. After $3$ half-lives, how many remain? [2 marks]