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Q.
The half-life of $^{215}At$ is $100\,\mu\,s$. The time taken for the radioactivity of sample of $^{215} At$ to decay to $\frac{1}{16}^{th}$ of its initial value is
Atoms
Solution:
N = $\frac{N_0}{16}$ and T = 100 $\mu$s
Using, $\frac{N}{N_0} = \left( \frac{1}{2} \right)^{t/T}$ we get $\frac{1}{16} = \left( \frac{1}{2} \right)^{t/T}$
or $\left( \frac{1}{2} \right)^4 = \left( \frac{1}{2} \right)^{t/T} $ or $\frac{t}{T} $ = 4 or $t$ = 4 T = 4 $\times$ 100 = 400 $\mu$s