Two radioactive 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=e(4λ−6λ)t=1e2λt;2λt=1⇒t=12λ

Two radioactive 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=e(4λ−6λ)t=1e2λt;2λt=1⇒t=12λ

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Two radioactive 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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$\frac{1}{2 λ} s$

$\frac{1}{10 λ} s$

$\frac{1}{5 λ} s$

$\frac{1}{8 λ} s$

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Detailed Solution

From $N = N_{0} e^{- λt} \frac{N_{1}}{N_{2}} = \frac{e^{- λ_{1} t}}{e^{- λ_{2} t}} = e^{(λ_{2} - λ_{1}) t}$
$\Rightarrow \frac{1}{e} = e^{(4 λ - 6 λ) t} = \frac{1}{e^{2 λt}};$

$2 λt = 1 \Rightarrow t = \frac{1}{2 λ}$

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