Question:
There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds ?
$(\sqrt{2}=1.414)$
Correct Option: , 2
Solution:
$\frac{\mathrm{N}}{\mathrm{N}_{0}}=\left(\frac{1}{2}\right)^{\frac{\mathrm{t}}{\mathrm{t}_{1 / 2}}}$
$\frac{\mathrm{N}}{10^{10}}=\left(\frac{1}{2}\right)^{\frac{30}{60}}$
$\Rightarrow \quad \mathrm{N}=10^{10} \times\left(\frac{1}{2}\right)^{\frac{1}{2}}=\frac{10^{10}}{\sqrt{2}} \approx 7 \times 10^{9}$