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13.Nuclei
hard
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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