JEE Main 2007
- Exam
- JEE Main
- Year
- 2007
- Subject
- Physics
- Chapter
- Nuclear Physics
JEE Main 2007 · Physics · Nuclear Physics
The half-life period of a radio-active element X is same as the...
The half-life period of a radio-active element is same as the mean life time of another radioactive element . Initially they have the same number of atoms. Then
Options
- A will decay faster than
- B will decay faster than
- C and have same decay rate initially
- D and decay at same rate always.
Correct answer
B. will decay faster than
Step-by-step solution
\mathrm{t}_{1/2}=\frac{\ln 2}{\lambda_{\mathrm{x}}} \tau_{\text{mean }}=\frac{1}{\lambda_{\mathrm{y}}} ; \frac{\mathrm{dN}}{\mathrm{dt}}=-\lambda \mathrm{N} \frac{ \ln 2}{\lambda_{\mathrm{x}}}=\frac{1}{\lambda_{\mathrm{y}}} \Rightarrow \lambda_{}=\lambda_{ }(0.6932) \Rightarrow \lambda_{}>\lambda_{}