(B) The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.For substance $A$, $N_A = N_0 e^{-5 \lambda t}$.For substance $

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.For substance $A$, $N_A = N_0 e^{-5 \lambda t}$.For substance $B$, $N_B = N_0 e^{-\lambda t}$.Given the ratio $\frac{N_A}{N_B} = (1/e)^2 = e^{-2}$.Substituting the expressions:$\frac{N_0 e^{-5 \lambda t}}{N_0 e^{-\lambda t}} = e^{-2}$$e^{-5 \lambda t + \lambda t} = e^{-2}$$e^{-4 \lambda t} = e^{-2}$Equating the exponents:$-4 \lambda t = -2$$t = \frac{2}{4 \lambda} = \frac{1}{2 \lambda}$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

Medium

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

WBJEE 2012 All WBJEE

A
$\frac{1}{\lambda}$
B
$\frac{1}{2 \lambda}$
C
$\frac{1}{3 \lambda}$
D
$\frac{1}{4 \lambda}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Nuclei

Subtopic

Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

Previous Year

WBJEE 2012 Paper All WBJEE years →

$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

Medium

View Solution

The half-life of a radioactive substance is $20 \ min$. The approximate time interval $(t_{2}-t_{1})$ between the time $t_{2}$,when $2/3$ of it has decayed,and time $t_{1}$,when $1/3$ of it has decayed,is (in $min$):

MediumAIIMS 2018

View Solution

The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is:

Medium

View Solution

The number of nuclei of a radioactive substance is $1000$ and $900$ at times $t = 0$ and $t = 2 \ s$,respectively. Then,the number of nuclei at time $t = 4 \ s$ will be:

Difficult

View Solution

At $t = 0$,the number of active nuclei in a sample is $N_0$. How many nuclei will decay in the time interval between its first mean life and second half-life?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

Similar Questions

$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

The half-life of a radioactive substance is $20 \ min$. The approximate time interval $(t_{2}-t_{1})$ between the time $t_{2}$,when $2/3$ of it has decayed,and time $t_{1}$,when $1/3$ of it has decayed,is (in $min$):

The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is:

The number of nuclei of a radioactive substance is $1000$ and $900$ at times $t = 0$ and $t = 2 \ s$,respectively. Then,the number of nuclei at time $t = 4 \ s$ will be:

At $t = 0$,the number of active nuclei in a sample is $N_0$. How many nuclei will decay in the time interval between its first mean life and second half-life?

Vedclass Test Series

Exam Paper Generator

Online Exam Module