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JAMB Physics 2021 Paper

Question : 16

Total: 40

Solution:

Concept:

A half-life is the time after which exactly half of the original radioactive atoms remain.

Explanation:

Let the half-life be

T_{1/2}

After

n

half-lives, the fraction remaining equals

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

The material left after

120

years is

\frac{1}{64}

Since

\frac{1}{64} = \left(\frac{1}{2}\right)^6

, the number of half-lives elapsed is

n = 6

Therefore,

120 \text{ years} = 6 \times T_{1/2}

Solving for

T_{1/2}

, we get

T_{1/2} = \frac{120 \text{ years}}{6} = 20 \text{ years}

Thus the half-life is

20

years.

Answer:

20 years.

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