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?
(Take $\sqrt{2}=1.414$)

• A. $4\times {10}^{10}$
• B. ${10}^5$
• C. $2\times {10}^{10}$
• D. $7\times {10}^9$

Answer 1

The correct option is D $7\times {10}^9$

Given :-
$N_o={10}^{10}$
$t=30\text{s}$
$t_{1/2}=1\text{min}=60\text{s}$

We know that :
$N=N_o{\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$
$\Rightarrow N={10}^{10}{\left(\frac{1}{2}\right)}^{\frac{30}{60}}=\frac{{10}^{10}}{\sqrt{2}}$
Or, $N=7\times {10}^9$