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JAMB Physics 2020 Paper

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Question : 38

Total: 38

A substance has half of 3 min. After 6 min, the count rate was observed to be 400. What was its count rate at zero time?

1600
1200
200
2400

Solution:

Concept:

Each half-life reduces the count rate by half.

Explanation:

Half-life

= 3\text{ min}

.

Time elapsed

= 6\text{ min}

.

Number of half-lives

= \frac{6}{3} = 2

.

After 2 half-lives, count rate

= N_0 \times \left(\frac{1}{2}\right)^2 = \frac{N_0}{4}

.

Given count rate after 6 min is

400

.

So,

\frac{N_0}{4} = 400

.

Multiplying both sides by

4

:

N_0 = 1600

.

Therefore, the count rate at zero time was

1600

.

Answer:

A.

1600

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