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  4. 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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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

NEETNEET 2018Nuclei

Solution:

Number of nuclei remaining $= 600 - 450 = 150$
$\frac{N}{N_{0}} = \left(\frac{1}{2}\right)^{n}$
$ \frac{150}{600} = \left(\frac{1}{2}\right)^{\frac{t}{t_{\frac{1}{2}}}}$
$ \left(\frac{1}{2}\right)^{2} = \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}$
$ t = 2t_{1/2} = 2 \times10 $
$ = 20 $ minute