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13.Nuclei
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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
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
$\frac{1}{2}({T_\alpha } + {T_\beta })$
(AIEEE-2012)
Solution
${T_{av}} = \frac{{{T_\alpha }{T_\beta }}}{{{T_\alpha } + {T_\beta }}}$
If $\alpha $ and $\beta $ are emitted simultaneously.
Standard 12
Physics
