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Q.

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?

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a

37%

b

50%

c

63%

d

69%

answer is C.

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Detailed Solution

$N = N_{0} e^{- λ t} time= \frac{1}{λ}$
$\frac{N}{N_{0}} = e^{- λ (\frac{1}{λ})}$
$\frac{N}{N_{0}} = e^{- 1} = \frac{1}{e}$
$(1 - \frac{N}{N_{0}}) \times 100 = (1 - \frac{1}{e}) \times 100 = (\frac{e - 1}{e}) \times 100$
$= (\frac{2.718 - 1}{2.718}) \times 100 = 63 %$

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