A radioactive sample has a half-life of 12\text{ minutes}. If its initial activity is 96\t… — JAMB UTME

A radioactive sample has a half-life of $12\text{ minutes}$ . If its initial activity is $96\text{ Bq}$ , what is the remaining activity of the sample, in $\text{Bq}$ , after an elapsed time of $36\text{ minutes}$ ?

Answer: 12 Bq

Answer

The remaining activity of the radioactive sample after

36\text{ minutes}

12\text{ Bq}

36\text{ minutes}

, exactly

3

half-lives elapse (

36 / 12 = 3

). The remaining activity reduces to

(1/2)^3 = 1/8

of the initial value, giving

96\text{ Bq} / 8 = 12\text{ Bq}

Step-by-Step Solution

Calculate the number of half-lives that have elapsed

n = 3

Divide the total elapsed time (

36\text{ minutes}

) by the half-life duration (

12\text{ minutes}

Calculate the remaining activity of the isotope

A = 12\text{ Bq}

After

n = 3

half-lives, the remaining activity fraction is

\left(\frac{1}{2}\right)^3 = \frac{1}{8}

. Multiplying initial activity

96\text{ Bq}

\frac{1}{8}

yields

12\text{ Bq}

Key Concept

Radioactive Decay Law and Half-life

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