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JEE Main 201219 MayOnline

Exam: JEE Main
Year: 2012
Date: 19 May
Mode: Online
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2012 · 19 May · Online · Physics · Nuclear Physics

The decay constants of a radioactive substance for α and β emission...

The decay constants of a radioactive substance for

\alpha

and

\beta

emission are

\lambda_\alpha

and

\lambda_\beta

respectively. If the substance emits

\alpha

and

\beta

simultaneously, then the average half life of the material will be

Options

A $\frac{2 T_\alpha T_\beta}{T_\alpha+T_\beta}$
B $T_\alpha+T_\beta$
C $\frac{T_\alpha T_\beta}{T_\alpha+T_\beta}$
D $\frac{1}{2}\left(T_\alpha+T_\beta \quad\right)$

Correct answer

C. $\frac{T_\alpha T_\beta}{T_\alpha+T_\beta}$

Step-by-step solution

T_{a v}=\frac{T_\alpha T_\beta}{T_\alpha+T_\beta}

If

\alpha

and

B

are emitted simultaneously.

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