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A radioactive nucleus has a half -life of 100 year. the number of nuclei at \mathrm{t=0} is \mathrm{N_0}. What will be the number of nuceli which have decayed in 300 years?
 

Option: 1

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


Option: 2

\frac{\mathrm{Na}}{2}


Option: 3

\mathrm{ \frac{3 N_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, \mathrm{n= ~number~ of~ half ~lives, n=\frac{300}{100}\Rightarrow n=3}
\begin{aligned} \therefore \text { Number of atoms decayed } & =\mathrm{N_0\left[1-\left(\frac{1}{2}\right)^3\right] }\\ & \mathrm{=N_0\left[1-\frac{1}{8}\right] }\\ & \mathrm{ =\frac{7 N_0}{8}} \end{aligned}

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