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Q.

Two radioactive material $A_{1}$ and $A_{2}$ have decay constant of $10 λ_{0}$ and $λ_{0}$ initially they have same
number of nuclei, then after time $\frac{1}{9 λ_{0}}$ the ratio of number of their undecayed nuclei will be :

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a

$\frac{\sqrt{e}}{1}$

b

$\frac{1}{e^{2}}$

c

$\frac{1}{e^{3}}$

d

$\frac{1}{e}$

answer is A.

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Detailed Solution

$\frac{N_{1}}{N_{2}} = \frac{e^{- λ_{1} t}}{e^{- λ_{2} t}} = e$

$(λ_{0} - 10 λ_{0}) \times \frac{1}{9 λ_{0}} = \frac{1}{e}$

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Two radioactive material A1 and A2 have decay constant of 10λ0 and λ0 initially they have same number of nuclei, then after time 19λ0 the ratio of number of their undecayed nuclei will be :