Search any question & find its solution
Question:
Answered & Verified by Expert
The half-life of a radioactive element $\mathrm{A}$ is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then :
Options:
Solution:
2472 Upvotes
Verified Answer
The correct answer is:
$\mathrm{B}$ will decay at a faster rate than $\mathrm{A}$.
$\mathrm{B}$ will decay at a faster rate than $\mathrm{A}$.
$\left(\mathrm{T}_{1 / 2}\right)_{\mathrm{A}}=\left(\mathrm{t}_{\text {mean }}\right)_{\mathrm{B}}$
$$
\Rightarrow \frac{0.693}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \Rightarrow \lambda_{\mathrm{A}}=0.693 \lambda_{\mathrm{B}}
$$
or $\lambda_{\mathrm{A}} < \lambda_{\mathrm{B}}$
Also rate of decay $=\lambda \mathrm{N}$
Initially number of atoms $(\mathrm{N})$ of both are equal but since $\lambda_{\mathrm{B}}>\lambda_{\mathrm{A}}$, therefore $\mathrm{B}$ will decay at a faster rate than $\mathrm{A}$
$$
\Rightarrow \frac{0.693}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \Rightarrow \lambda_{\mathrm{A}}=0.693 \lambda_{\mathrm{B}}
$$
or $\lambda_{\mathrm{A}} < \lambda_{\mathrm{B}}$
Also rate of decay $=\lambda \mathrm{N}$
Initially number of atoms $(\mathrm{N})$ of both are equal but since $\lambda_{\mathrm{B}}>\lambda_{\mathrm{A}}$, therefore $\mathrm{B}$ will decay at a faster rate than $\mathrm{A}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.