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13.Nuclei
medium
In a $RA$ element the fraction of initiated amount remaining after its mean life time is
A
$1 - \frac{1}{e}$
B
$\frac{1}{e^2}$
C
$\frac{1}{e}$
D
$1- \frac{1}{e^2}$
Solution
Given,
a Radioactive element
mean life time $=\frac{1}{\lambda}$
Let $A _0=$ initial no. of nuclie
afiuhter any time $= t$, no of nuclie left $= A _{ t }$
$A _{ t }= A _0 e ^{-\lambda t }, \lambda=$ decay constant
$A _{ t }= A _0 e ^{-\lambda \times \frac{1}{\lambda} \quad \therefore\quad t _{\text {mean }}}=\frac{1}{\lambda}$
$A _{ t }= A _0 e ^{-1}$
$A _{ t }=\frac{ A _0}{ e }$
$\left(\frac{A_*}{A_0}\right)=\frac{1}{e}=$ fraction of ammount left
Standard 12
Physics
