Calculating Radioactive Decay Flashcards

All 4 cards in this deck

What fraction of the original nuclei remains after $n$ half-lives?

$\left(\frac{1}{2}\right)^{n}$

e.g. after 3 half-lives, $\frac{1}{8}$ remains.

What are the steps to find the net decline in activity as a ratio after a given number of half-lives?

e.g. after 3 half-lives

1. Halve once per half-life: $1 \rightarrow \frac{1}{2} \rightarrow \frac{1}{4} \rightarrow \frac{1}{8}$
2. Fraction remaining $= \frac{1}{8}$
3. Net decline as a ratio $= 1:8$

What are the steps to find how long it takes for activity to fall to a given fraction?

e.g. fall to one quarter, half-life 60 s

1. Count the halvings: $1 \rightarrow \frac{1}{2} \rightarrow \frac{1}{4}$, so 2 half-lives
2. Multiply by the half-life: $2 \times 60 = 120$ s

True or false? A net decline of 1:16 means four half-lives have passed.

True. $\frac{1}{2}$ four times gives $\frac{1}{16}$ remaining.