A radioactive isotope used in a hospital scan has a half-life of 6 hours. Immediately after preparation, a sample has a background-corrected activity of 960 Bq. Assuming no more of the isotope is added, how long after preparation will the activity first fall to 60 Bq?

IGCSE Physics 0625: Half-Life Calculation for a Hospital Radioisotope

The activity halves every half-life. Starting from 960 Bq, repeatedly halve until reaching 60 Bq:

$960 \to 480 \to 240 \to 120 \to 60$

This takes 4 halvings (half-lives) to go from 960 Bq down to 60 Bq.

Each half-life is 6 hours, so the total time is:

$4 \times 6 = 24 \text{ hours}$

The activity first falls to 60 Bq after 24 hours, so the answer is option C.

Option	Time	Activity at that time	Why it’s wrong
A	6 hours	$960 \div 2 = 480$ Bq	Only 1 half-life has passed; the activity is still far above 60 Bq.
B	18 hours	$960 \div 2^3 = 120$ Bq	Only 3 half-lives have passed; the activity has not yet fallen to 60 Bq.
D	30 hours	$960 \div 2^5 = 30$ Bq	This is 5 half-lives, by which time the activity has already fallen below 60 Bq, so 60 Bq was reached earlier.