Radioactive material A has decay constant 8 λ and material B has decay constant λ . Initially they have the same number of nuclei. After what time, the ratio of number of nuclei of material A to that

Question

Radioactive material A has decay constant 8 λ and material B has decay constant λ . Initially they have the same number of nuclei. After what time, the ratio of number of nuclei of material A to that B will be 1 e ? NEET 2017

TestHub · Accepted Answer

Number of undecayed nuclei present at time $t$ is

$N = N_{0} e^{- λ t}$ , here $N_{0}$ is the number of radioactive nuclei in sample at time $t = 0$ .

So for $A, N_{A} = N_{0} e^{- 8 λ t}$

for $B, N_{B} = N_{0} e^{- λ t}$

given $\frac{N_{A}}{N_{B}} = \frac{1}{e}$

Then

$\frac{N_{A}}{N_{B}} = \frac{N_{0} e^{- 8 λ t}}{N_{0} e^{- λ t}}$

$\frac{1}{e} = e^{- 7 λ t}$

$- 1 = - 7 λ t$

$t = \frac{1}{7 λ}$

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