Half life period of a radioactive sample is T . Let x fraction disintegrates in time 't' . H

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Half life period of a radioactive sample is $T$. Let $x$ fraction disintegrates in time $'t'$. How much fraction will decay in $'\frac{t}{2}'$ time

A

$\left( {\frac{x}{2}} \right)$

B

$\left( {\frac{x}{{\sqrt 2 }}} \right)$

C

$1 - \left( {\frac{x}{{\sqrt 2 }}} \right)$

D

$1 - \left( {\sqrt {1 - x} } \right)$

Solution

At time $t,$ active fraction $=1-x$

so at time $\frac{t}{2},$ Active fraction $=\sqrt{1-x}$

so at time $\frac{t}{2},$ decay fraction $=1-\sqrt{1-x}$

Standard 12

Physics

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