The half life of a radium is about 1600 years. Of $100 \mathrm{~g}$ of radium existing now 25 g will remain…
The half life of a radium is about 1600 years. Of $100 \mathrm{~g}$ of radium existing now 25 g will remain unchanged after :-
4800 years
6400 years
2400 years
3200 years
Solution
Applying the formula
$\begin{aligned}
N & =N_0\left(\frac{1}{2}\right)^n \\
\Rightarrow \quad \frac{N}{N_0} & =\left(\frac{1}{2}\right)^n
\end{aligned}$
$\Rightarrow \frac{25}{100}=\left(\frac{1}{2}\right)^n \Rightarrow n=2$
$\therefore$ Total time is $2 \times 1600=3200$ year