Q136 / 200 · NEET 2004 · Physics

The half life of a radium is about 1600 years. Of $100 \mathrm{~g}$ of radium existing now 25 g will remain unchanged after :-

  • A
    4800 years
  • B
    6400 years
  • C
    2400 years
  • Correct answer
    D
    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

Hence, the correct answer is option: 'D'.

Relevant Questions