Q128 / 160 · JIPMER 2010 · Physics

The half-life of a radio-isotope is 4 h . If initial mass of the isotope was 200 g , then mass remaining after 24 h will be

A
1.042 g
B
2.084 g
Correct answer
C
3.125 g
D
4.167 g

Solution

$\begin{aligned} & M=M_0\left(\frac{1}{2}\right)^{t / 1 / 2} \\ & \therefore \quad M=200\left(\frac{1}{2}\right)^{24 / 4}=200\left(\frac{1}{2}\right)^6=\frac{200}{64}=3.125 \mathrm{~g}\end{aligned}$

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

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