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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2013 · 22 April · Online · Physics · Nuclear Physics

The half-life of a radioactive element A is the same as the...

The half-life of a radioactive element A\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

  1. AA and B decay at the same rate always.
  2. BA and B\mathrm{B} decay at the same rate initially.
  3. CA will decay at a faster rate than B.
  4. DB\mathrm{B} will decay at a faster rate than A\mathrm{A}.

Correct answer

D. B\mathrm{B} will decay at a faster rate than A\mathrm{A}.

Step-by-step solution

\left(\mathrm{T}_{1/2}\right)_{\mathrm{A}}=(tmean )B\left(\mathrm{t}_{\text{mean }}\right)_{\mathrm{B}} ⇒0.693λA=1λB⇒λA=0.693λB\Rightarrow \frac{0.693}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \Rightarrow \lambda_{\mathrm{A}}=0.693 \lambda_{\mathrm{B}} or λA<λB\lambda_{\mathrm{A}} < \lambda_{\mathrm{B}} Also rate of decay =λN=\lambda \mathrm{N} Initially number of atoms (N)(\mathrm{N}) of both are equal but since λB>λA\lambda_{\mathrm{B}}>\lambda_{\mathrm{A}}, therefore B\mathrm{B} will decay at a faster rate than A\mathrm{A}
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