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 ?

Question

Aicharya · 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}

Radioactive material A has decay constant 8 λ and material B has decay constant λ . Initially they have the…

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