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  • A radioactive nucleus has a half -life of 100 year. the number of nuclei at  t=0 is . what will be the number of nuclei which have decayed

A radioactive nucleus has a half -life of 100 year. the number of nuclei at  t=0 is N_{o}. what will be the number of nuclei which have decayed in 300 years?

Option: 1

\mathrm{ \frac{7 N_0}{8}}


Option: 2

\mathrm{ \frac{ N_0}{2}}


Option: 3

\mathrm{ \frac{ 3N_0}{4}}


Option: 4

\mathrm{ \frac{ N_0}{8}}


Answers (1)

best_answer

Here, Number of atoms decayed = \mathrm{ N_0\left[1-\left(\frac{1}{2}\right)^n\right] } where,
n= number of half lives, \mathrm{ n=\frac{300}{100} n=3 }

\mathrm{ \begin{aligned} \therefore \text { Number of atoms decayed } & =N_0\left[1-\left(\frac{1}{2}\right)^3\right] \\ & =M_0\left[1-\frac{1}{8}\right] \\ & =\frac{7 N_0}{8} \text { Ans. } \end{aligned} }

Posted by

rishi.raj

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