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WAEC Physics 2022 Paper

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Question : 35

Total: 50

The half-life of a radioactive substance is 15 hours. If at some instance, the sample has a mass of 512 g , calculate the time it will take

\frac{7}{8}

of the sample to decay

15 hours
30 hours
45 hours
60 hours

Solution:

Concept:

After

n

half-lives, the remaining mass is

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

of the original mass.

Explanation:

When

\frac{7}{8}

of the sample decays, only

\frac{1}{8}

of the original sample remains.

This remaining fraction is written as:

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

Since

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

, the number of half-lives is

n = 3

.

Each half-life lasts

15

hours, so the total time is:

3 \times 15 = 45 \text{ hours}

Thus, the sample takes

45

hours for

\frac{7}{8}

of it to decay.

Answer:

45

hours (Option C).

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