First slide

Radio activity

Question

Half life of a radio active element is 1200 yrs. It m₀ gm of radio active element existing now, m₀/4 gm will remain radio active after

Moderate

A

600 years
B

4800 years
C

2400 years
D

2800 years

Solution

$\frac{N}{N_{0}} = \frac{1}{(2)^{t / T}} \Rightarrow \frac{m_{0} / 4}{m_{0}} = \frac{1}{(2)^{t / T}} \Rightarrow \frac{1}{(2)^{2}} = \frac{1}{(2)^{t / T}}$
$\Rightarrow t / T = 2 \Rightarrow t = 2 \times 1200 years$
= 2400 years

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