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Q.

For a radioactive material, half-life is $10$ minutes. If initially there are $600$ number of nuclei, the time taken (in minutes) for the disintegration of $450$ nuclei is

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a

$30$

b

$15$

c

$20$

d

$10$

answer is A.

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Detailed Solution

Number of nuclei remaining $N = 600 - 450 = 150$

According to the law of radioactive decay, $\frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}$

${(\frac{1}{2})}^{2} = {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}$

$t = 2 T_{1 / 2} = 20$ minutes

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