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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

A

30

B

10

C

20

D

15

Step-by-Step Solution

Number of nuclei remaining = 600−450=150600 - 450 = 150. Using the formula NN0=(12)n\frac{N}{N_0} = (\frac{1}{2})^n, where n=tt1/2n = \frac{t}{t_{1/2}}, we get 150600=(12)t10\frac{150}{600} = (\frac{1}{2})^{\frac{t}{10}}. Thus, 14=(12)t10\frac{1}{4} = (\frac{1}{2})^{\frac{t}{10}}, which implies (12)2=(12)t10(\frac{1}{2})^2 = (\frac{1}{2})^{\frac{t}{10}}. Therefore, t10=2\frac{t}{10} = 2, so t=20t = 20 minutes.

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