Two radioactive materials $X_1$ and $X_2$ have decay constants $5 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. After time $t$,the ratio of the number of nuclei of $X_1$ to that of $X_2$ is $\frac{1}{e}$. Then $t$ is equal to:
- A$\frac{\lambda}{2}$
- B$\frac{e}{\lambda}$
- C$\lambda$
- D$\frac{1}{4 \lambda}$
Explore More
Similar Questions
The radioactivity of a sample at time $T_1$ is $R_1$ and at time $T_2$ is $R_2$. If the mean life of the sample is $T$,then the number of nuclei disintegrated in the time interval $(T_2 - T_1)$ is:
Medium
View SolutionThe 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 SolutionAt $t = 0$,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 SolutionThere are $10^{10}$ radioactive nuclei in a given radioactive element. Its half-life time is $1 \text{ minute}$. How many nuclei will remain after $30 \text{ seconds}$? $(\sqrt{2} = 1.414)$
Two radioactive materials $Y_1$ and $Y_2$ initially contain the same number of nuclei. Their decay constants are $9 \lambda \ s^{-1}$ and $6 \lambda \ s^{-1}$ respectively. The time after which the ratio of the number of undecayed nuclei of $Y_1$ and $Y_2$ becomes $\frac{1}{e}$ is:
DifficultAP EAMCET 2017
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo