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 :-
  1. 4800 years
  2. 6400 years
  3. 2400 years
  4. 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

Asked in: NEET 2004

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