During mean life of a radioactive element. the fraction that distintegrates is

e

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\frac{1}{e}

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\frac{e - 1}{e}

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\frac{e}{e - 1}

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Solution

The correct option is C $\frac{e - 1}{e}$
By using $N = N_{0} e^{- λ t}$ . . . . . ..(1)
Average life time, $t = \frac{1}{λ}$
From equation (1),
$N = N_{0} e^{- λ / λ} = N_{0} e^{- 1}$
$\frac{N}{N_{0}} = \frac{1}{e}$
Now, disintegrated fraction,
$1 - \frac{N}{N_{0}} = 1 - \frac{1}{e}$
$= \frac{e - 1}{e}$
The correct option is C.

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