Decay constants of two radio-active samples A and B are 15x and 3x respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in A and B after a time (1/6x) is .

Question

Decay constants of two radio-active samples A and B are 15x and 3x respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in A and B after a time (1/6x) is . (A) e (B) e2 (C) e-1 (D) e-2

Tardigrade Admin · Accepted Answer

N1=N01 e-λ1 t=N0 e-15 x × (1/6 x)=N0 e-5 / 2 and N2=N02 e-λ2 t=N0 e-3 x × (1/6 x)=N0 e-1 / 2 ∴ (N1/N2)=e-2

Q. Decay constants of two radio-active samples $A$ and $B$ are $15 x$ and $3 x$ respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $\frac{1}{6 x}$ is .

$e$

$e^{2}$

$e^{- 1}$

$e^{- 2}$

$N_{1} = N_{01} e^{- λ_{1} t} = N_{0} e^{- 15 x \times \frac{1}{6 x}} = N_{0} e^{- 5/2}$
and $N_{2} = N_{02} e^{- λ_{2} t} = N_{0} e^{- 3 x \times \frac{1}{6 x}} = N_{0} e^{- 1/2}$
$∴ \frac{N _{1}}{N _{2}} = e^{- 2}$

Q. Decay constants of two radio-active samples A and B are 15x and 3x respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in A and B after a time 6x1​ is .

e

e2

e−1

e−2

N1​=N01​e−λ1​t=N0​e−15x×6x1​=N0​e−5/2 and N2​=N02​e−λ2​t=N0​e−3x×6x1​=N0​e−1/2 ∴N2​N1​​=e−2

Q. Decay constants of two radio-active samples $A$ and $B$ are $15 x$ and $3 x$ respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $\frac{1}{6 x}$ is .

$e$

$e^{2}$

$e^{- 1}$

$e^{- 2}$

$N_{1} = N_{01} e^{- λ_{1} t} = N_{0} e^{- 15 x \times \frac{1}{6 x}} = N_{0} e^{- 5/2}$
and $N_{2} = N_{02} e^{- λ_{2} t} = N_{0} e^{- 3 x \times \frac{1}{6 x}} = N_{0} e^{- 1/2}$
$∴ \frac{N _{1}}{N _{2}} = e^{- 2}$