Two radioactive materials X1and X2 contain same number of nuclei. If 8λs−1 and 3λs−1 are the decay constants of X1& X2 respectively. The ratio of number of nuclei undecayed of x1 to that of x2 will be 1e after a time

x1x2=N0e−(8λ)tN0e−(3λ)t=1e⇒e−(5λ)t=e−1,t=15λ

Two radioactive materials X1and X2 contain same number of nuclei. If 8λs−1 and 3λs−1 are the decay constants of X1& X2 respectively. The ratio of number of nuclei undecayed of x1 to that of x2 will be 1e after a time

x1x2=N0e−(8λ)tN0e−(3λ)t=1e⇒e−(5λ)t=e−1,t=15λ

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Two radioactive materials X₁and X₂ contain same number of nuclei. If $8 {λs}^{- 1}$ and $3 {λs}^{- 1}$ are the decay constants of X₁& X₂respectively. The ratio of number of nuclei undecayed of x₁ to that of x₂ will be $\frac{1}{e}$ after a time

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$\frac{1}{2 λ} s$

$\frac{1}{10 λ} s$

$\frac{1}{5 λ} s$

$\frac{1}{8 λ} s$

answer is C.

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$\frac{x_{1}}{x_{2}} = \frac{N_{0} e^{- (8 λ) t}}{N_{0} e^{- (3 λ) t}} = \frac{1}{e} \Rightarrow e^{- (5 λ) t} = e^{- 1}, t = \frac{1}{5 λ}$

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Two radioactive materials X1and X2 contain same number of nuclei. If 8λs−1 and 3λs−1 are the decay constants of X1& X2 respectively. The ratio of number of nuclei undecayed of x1 to that of x2 will be 1e after a time

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Two radioactive materials X₁and X₂ contain same number of nuclei. If $8 {λs}^{- 1}$ and $3 {λs}^{- 1}$ are the decay constants of X₁& X₂respectively. The ratio of number of nuclei undecayed of x₁ to that of x₂ will be $\frac{1}{e}$ after a time