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JAMB Chemistry 2019 Paper

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Question : 35

Total: 80

A radioactive nucleus has a half-life of 20 years, starting with 100,000 particles, how many particles will be left exactly at the end of 40 years

75,000 particles
35,000 particles
25,000 particles
50,000 particles

Solution:

Concept:

Radioactive decay halves the number of particles after every half-life period.

Explanation:

The half-life is given as

t_{\frac{1}{2}} = 20

years.

Starting amount

N_0 = 100{,}000

particles.

After 40 years, exactly two half-lives have passed:

\frac{40}{20} = 2

.

For each half-life, the remaining amount is multiplied by

\frac{1}{2}

.

After 40 years:

N = 100{,}000 \times \left(\frac{1}{2}\right)^2

.

This gives

N = 100{,}000 \times \frac{1}{4} = 25{,}000

particles.

Answer:

25{,}000

particles, which is option C.

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