For a radioactive material,the half-life is 1 | vedclass

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(A) The number of nuclei remaining after disintegration is given by $N = N_{0} - N_{	ext{disintegrated}}$.Given $N_{0} = 600$ and $N_{	ext{disintegr

Vedclass · Accepted Answer

$20$

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(A) The number of nuclei remaining after disintegration is given by $N = N_{0} - N_{	ext{disintegrated}}$.Given $N_{0} = 600$ and $N_{	ext{disintegrated}} = 450$,the remaining nuclei $N = 600 - 450 = 150$.According to the law of radioactive decay,$\frac{N}{N_{0}} = \left(\frac{1}{2}ight)^{\frac{t}{T_{1/2}}}$,where $T_{1/2} = 10$ minutes.Substituting the values: $\frac{150}{600} = \left(\frac{1}{2}ight)^{\frac{t}{10}}$.This simplifies to $\frac{1}{4} = \left(\frac{1}{2}ight)^{\frac{t}{10}}$.Since $\frac{1}{4} = \left(\frac{1}{2}ight)^{2}$,we have $\left(\frac{1}{2}ight)^{2} = \left(\frac{1}{2}ight)^{\frac{t}{10}}$.Equating the exponents: $2 = \frac{t}{10}$,which gives $t = 20$ minutes.

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

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