(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

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 →

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5\, \text{minutes}$. The time (in minutes) at which the activity reduces to half of its initial value is

Difficult

View Solution

$A$ nucleus has a half-life of $30 \; min$. At $3 \; PM$, its decay rate was measured as $120000 \; cps$. What is the decay rate in $cps$ at $5 \; PM$?

MediumKVPY 2010

View Solution

Define the disintegration rate or radioactivity of a sample and obtain the relation $R = \lambda N$ and define its different units.

Medium

View Solution

Which one of the following nuclei has a shorter mean life?

EasyKCET 2019

View Solution

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

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

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5\, \text{minutes}$. The time (in minutes) at which the activity reduces to half of its initial value is

$A$ nucleus has a half-life of $30 \; min$. At $3 \; PM$, its decay rate was measured as $120000 \; cps$. What is the decay rate in $cps$ at $5 \; PM$?

Define the disintegration rate or radioactivity of a sample and obtain the relation $R = \lambda N$ and define its different units.

Which one of the following nuclei has a shorter mean life?

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module