First slide

Radio activity

Question

If $\frac{7}{8}$ th part of a radio active element decays in 168 sec, its half life is

Moderate

A

16 S
B

56 S
C

128 S
D

21 S

Solution

$N = \frac{N_{0}}{{(2)}^{t / t_{1 / 2}}}$
$∴ N_{0} - \frac{7 N_{0}}{8} = \frac{N_{0}}{{(2)}^{t / t_{1 / 2}}} \Rightarrow {(2)}^{t / t_{1 / 2}} = 8 = {(2)}^{3}$
$∴ t_{1 / 2} = \frac{t}{3} = \frac{168}{3} \sec = 56 \sec$

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