(C) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}}$.For substance $A$,$n_A = \frac{80}{20} = 4$.For substance $B$,$n_B = \frac{80}{40

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

(C) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}}$.For substance $A$,$n_A = \frac{80}{20} = 4$.For substance $B$,$n_B = \frac{80}{40} = 2$.The number of remaining nuclei is given by $N = N_0 \left( \frac{1}{2} \right)^n$.Since initial numbers $N_0$ are equal,the ratio is $\frac{N_A}{N_B} = \frac{N_0 (1/2)^{n_A}}{N_0 (1/2)^{n_B}} = \frac{(1/2)^4}{(1/2)^2} = \frac{2^2}{2^4} = \frac{4}{16} = \frac{1}{4}$.Thus,the ratio is $1 : 4$.

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

Medium

Half-lives of two radioactive substances $A$ and $B$ are $20 \text{ minutes}$ and $40 \text{ minutes}$ respectively. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \text{ minutes}$,the ratio of the remaining number of $A$ and $B$ nuclei is:

AIPMT 1998 All AIPMT

A
$1 : 16$
B
$4 : 1$
C
$1 : 4$
D
$1 : 1$

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

AIPMT 1998 Paper All AIPMT years →

If a radioactive element having a half-life of $30 \ min$ is undergoing beta decay,the fraction of the radioactive element that remains undecayed after $90 \ min$ will be:

EasyJEE MAIN 2023

View Solution

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

Medium

View Solution

$A$ radioactive isotope $X$ with a half-life of $1.37 \times 10^9$ years decays to $Y$,which is stable. $A$ sample of rock from the moon was found to contain both the elements $X$ and $Y$ in the ratio of $1 : 7$. The age of the rock is

Medium

View Solution

The $S.I.$ unit of radioactivity is

Easy

View Solution

The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half-life of the specimen is $T,$ the number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to

Difficult

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

Half-lives of two radioactive substances $A$ and $B$ are $20 \text{ minutes}$ and $40 \text{ minutes}$ respectively. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \text{ minutes}$,the ratio of the remaining number of $A$ and $B$ nuclei is:

Similar Questions

If a radioactive element having a half-life of $30 \ min$ is undergoing beta decay,the fraction of the radioactive element that remains undecayed after $90 \ min$ will be:

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

$A$ radioactive isotope $X$ with a half-life of $1.37 \times 10^9$ years decays to $Y$,which is stable. $A$ sample of rock from the moon was found to contain both the elements $X$ and $Y$ in the ratio of $1 : 7$. The age of the rock is

The $S.I.$ unit of radioactivity is

The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half-life of the specimen is $T,$ the number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module