(D) Given: $(T_{1/2})_A = (\tau)_B$, where $\tau$ is the mean life.We know that $T_{1/2} = \frac{0.693}{\lambda}$ and $\tau = \frac{1}{\lambda}$.There

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

$B$ will decay at a faster rate than $A.$

(D) Given: $(T_{1/2})_A = (\tau)_B$, where $\tau$ is the mean life.We know that $T_{1/2} = \frac{0.693}{\lambda}$ and $\tau = \frac{1}{\lambda}$.Therefore, $\frac{0.693}{\lambda_A} = \frac{1}{\lambda_B}$.This implies $\lambda_A = 0.693 \lambda_B$, which means $\lambda_A The rate of decay is given by $R = \lambda N$.Initially, the number of atoms $N$ is the same for both elements.Since $\lambda_B > \lambda_A$, the decay rate $R_B = \lambda_B N$ will be greater than $R_A = \lambda_A N$.Thus, $B$ will decay at a faster rate than $A$.

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

Medium

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

JEE MAIN 2013 All JEE MAIN

A
$A$ and $B$ decay at the same rate always.
B
$A$ and $B$ decay at the same rate initially.
C
$A$ will decay at a faster rate than $B.$
D
$B$ will decay at a faster rate than $A.$

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

JEE MAIN 2013 Paper All JEE MAIN years →

In a fossil bone,the ratio of $^{14}C : ^{12}C$ is $1/16$ of the ratio found in a living animal. If the half-life of $^{14}C$ is $5730 \text{ years}$,find the age of the fossil bone in years.

Easy

View Solution

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6\%$ of the time it decays by $\alpha$-decay and $33.3\%$ of the time it decays by $\beta$-decay. If the effective half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay? (in years)

Difficult

View Solution

The count rate for $10 \, g$ of radioactive material was measured at different times and this has been shown in the graph. The half-life of the material and the total count in the first half-life period respectively are:

Difficult

View Solution

$A$ radioactive material has an initial amount $16 \, gm$. After $120 \, days$ it reduces to $1 \, gm$. The half-life of the radioactive material is .......... $days$.

Medium

View Solution

Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ 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:

EasyAP EAMCET 2009

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

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

Similar Questions

In a fossil bone,the ratio of $^{14}C : ^{12}C$ is $1/16$ of the ratio found in a living animal. If the half-life of $^{14}C$ is $5730 \text{ years}$,find the age of the fossil bone in years.

The count rate for $10 \, g$ of radioactive material was measured at different times and this has been shown in the graph. The half-life of the material and the total count in the first half-life period respectively are:

$A$ radioactive material has an initial amount $16 \, gm$. After $120 \, days$ it reduces to $1 \, gm$. The half-life of the radioactive material is .......... $days$.

Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module