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13.Nuclei
medium
A radioactive substance has a half-life of $1$ year. The fraction of this material, that would remain after $5$ years will be
A
$\frac{1}{{32}}$
B
$\frac{1}{5}$
C
$\frac{1}{2}$
D
$\frac{4}{5}$
Solution
(a) Number of half lives $n = \frac{5}{1} = 5$
Now $\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n} $
$\Rightarrow \frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^5} = \frac{1}{{32}}$
Standard 12
Physics
