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  • There, are radioactive nuclei in a given radioactive element. Its half-life time

There, are \mathrm{10^{10} }radioactive nuclei in a given radioactive element. Its half-life time is 1 minute. How many nuclei will remain after 30 seconds?
[Take \mathrm{\sqrt{2}} =1.414 & \mathrm{\frac{1}{\sqrt{2}}}=0.7 .7]

Option: 1

10^5


Option: 2

2 \times 10^{10}


Option: 3

7 \times 10^9


Option: 4

4 \times 10^{20}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \lambda=\frac{\ln 2}{T_{1 / 2}}=\frac{0.693}{T_{1 / 2}} \\ & N=N_0 e^{-\lambda t}=\frac{N_0}{2^n}, \text { (whore } n=\begin{array}{c} \text { no. of Half } \\ \text { cycles }) \end{array} \\ & N=\frac{10^{10}}{2^{1 / 2}}=\frac{10^{10}}{1.414} \\ & N=\frac{10 \times 10^9}{1.414} \\ & N=\frac{10}{\sqrt{2}} \times 10^9=7 \times 10^9 \text { Ans } \end{aligned}}

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