First slide

Radio activity

Question

During mean life of a radioactive element, the fraction that disintegrates is

Moderate

A

e
B

$\frac{1}{e}$
C

$\frac{e - 1}{e}$
D

$\frac{e}{e - 1}$

Solution

By using $N = N_{0} e^{- λt}$ and average life time $t = \frac{1}{λ},$
$N = N_{0} e^{- λ x 1 / λ} = N_{0} e^{- 1} \Rightarrow \frac{N}{N_{0}} = e^{- 1} = \frac{1}{e}$
Now disintegrated fraction $= 1 - \frac{N}{N_{0}} = 1 - \frac{1}{e} = \frac{e - 1}{e}$

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