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13.Nuclei
medium
If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is
A
$\frac{1}{2}$
B
$\frac{3}{4}$
C
$\frac{1}{{\sqrt 2 }}$
D
$\frac{{\sqrt 2 - 1}}{{\sqrt 2 }}$
Solution
(c)Fraction remains after $n$ half lives
$\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n} = {\left( {\frac{1}{2}} \right)^{t/T}}$
$\therefore$ $\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{\frac{{T/2}}{T}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}$
Standard 12
Physics
