Two radioactive materials X1 and X2 have decay constants 10 λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1 / e after a time

Question

Two radioactive materials X1 and X2 have decay constants 10 λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1 / e after a time (A) (1 / 10 λ) (B) 1 /(11 λ) (C) 11 /(10 λ) (D) 1 /(9 λ)

Tardigrade Admin · Accepted Answer

N1=N0 e-10 λ t and N2=N0 e-λ t ⇒ (N1/N2)=(1/e)=e-1 =e(-10 λ+λ) t =e-9 λ t ⇒ t=(1/9 λ)

Q. Two radioactive materials $X_{1}$ and $X_{2}$ have decay constants $10 λ$ and $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_{1}$ to that of $X_{2}$ will be $1/ e$ after a time

$(1/10 λ)$

$1/ (11 λ)$

$11/ (10 λ)$

$1/ (9 λ)$

$N_{1} = N_{0} e^{- 10 λ t}$
and $N_{2} = N_{0} e^{- λ t}$
$\Rightarrow \frac{N _{1}}{N _{2}} = \frac{1}{e} = e^{- 1} = e^{(- 10 λ + λ) t}$
$= e^{- 9 λ t}$
$\Rightarrow t = \frac{1}{9 λ}$

Q. Two radioactive materials X1​ and X2​ have decay constants 10λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1​ to that of X2​ will be 1/e after a time

(1/10λ)

1/(11λ)

11/(10λ)

1/(9λ)