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

Correct answer: D. 3200 years Applying the formula aligned N & =N_0 ((1)/(2))^n (N)/(N_0)& =((1)/(2))^n aligned (25)/(100)=((1)/(2))^ n n=2 Total time is 2 × 1600=3200 year

NEET 2004

Exam: NEET
Year: 2004
Subject: Physics
Chapter: Nuclear Physics

NEET 2004 · Physics · Nuclear Physics

The half life of a radium is about 1600 years. Of 100 ~g of radium...

The half life of a radium is about 1600 years. Of

100 \mathrm{~g}

of radium existing now 25 g will remain unchanged after :-

Options

A4800 years
B6400 years
C2400 years
D3200 years

Correct answer

D. 3200 years

Step-by-step 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

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