Two radio active materials X1 and X2 contain same number of nuclei. If 6λs−1 and 4λs−1 are the decay constants of X1 and X2 respectively, The ratio of number of nuclei undecayed of X1 to that of X2 will be 1/e after a time

From N=N0e−λtN1N2=e−λ1te−λ2t=eλ2−λ1t⇒ 1e=e4λ−6λt=1e2λt; 2λt=1⇒t=12λ

Two radio active materials X1 and X2 contain same number of nuclei. If 6λs−1 and 4λs−1 are the decay constants of X1 and X2 respectively, The ratio of number of nuclei undecayed of X1 to that of X2 will be 1/e after a time

From N=N0e−λtN1N2=e−λ1te−λ2t=eλ2−λ1t⇒ 1e=e4λ−6λt=1e2λt; 2λt=1⇒t=12λ

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Two radio active materials X₁ and X₂ contain same number of nuclei. If $6 λ s^{- 1}$ and $4 λ s^{- 1}$ are the decay constants of X₁ and X₂ respectively, The ratio of number of nuclei undecayed of X₁ to that of X₂ will be 1/e after a time

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$\frac{1}{2 λ} s$

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$\frac{1}{8 λ} s$

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From $N = N_{0} e^{- λ t} \frac{N_{1}}{N_{2}} = \frac{e^{- λ_{1} t}}{e^{- λ_{2} t}} = e^{(λ_{2} - λ_{1}) t}$

$\Rightarrow \frac{1}{e} = e^{(4 λ - 6 λ) t} = \frac{1}{e^{2 λ t}}; 2 λ t = 1 \Rightarrow t = \frac{1}{2 λ}$

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Two radio active materials X1 and X2 contain same number of nuclei. If 6λs−1 and 4λs−1 are the decay constants of X1 and X2 respectively, The ratio of number of nuclei undecayed of X1 to that of X2 will be 1/e after a time

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Two radio active materials X₁ and X₂ contain same number of nuclei. If $6 λ s^{- 1}$ and $4 λ s^{- 1}$ are the decay constants of X₁ and X₂ respectively, The ratio of number of nuclei undecayed of X₁ to that of X₂ will be 1/e after a time