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13.Nuclei
hard
The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^9 s$. The mass of an atom of this radioisotope is $10^{-25} kg$. The mass (in $mg$ ) of the radioactive sample is
A
$1$
B
$2$
C
$3$
D
$4$
(IIT-2011)
Solution
Given: $\frac{ dN }{ dt }=10^{10}$
Mean Life $=10^9 s$
$\frac{1}{\lambda}=10^9 s$
$\lambda=10^{-9} s^{-1}$
FIrst order decay:
$\frac{ dN }{ dt }=\lambda N$
$\lambda N =10^{10}$
$N=10^{17}$
Mass of Radioactive sample $=10^{19} \times 10^{-25} kg=10^{-6} kg$
$M =10^{-6} kg=10^{-3} gms =1 mg$
Standard 12
Physics
