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>>First Order Radioactive Decay
>> $Using a nuclear counter the count rate o$

Question

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t = 0$ it was $1600$ counts per second and $t = 8$ seconds it was $100$ counts per second. The count rate observed, as counts per second, at $t = 6$ seconds is close to

A

$150$

B

$360$

C

$200$

D

$400$

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Updated on : 2022-09-05

Solution

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Correct option is C)

At $t = 0, A_{0} = \frac{d N}{d t} = 1600 C / s$
at $t = 8 s, A = 100 C / s$
$\frac{A}{A _{0}} = \frac{1}{1 6}$ in $8 s e c$
Therefore half life is $t_{1 / 2} = 2 s e c$
$∴$ Activity at $t = 6$ will be $1600 (\frac{1}{2})^{3}$
$= 200 C / s$
$∴$ correct answer is $(3)$ .

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