Q: The half-life of ^{215}At is 100 μs. The time taken for the activity of a sample of ^{215}At to decay to 1/16th of its initial value is

(A) 400 μs

(B) 63 μs

(C) 40 μs

(D) 300 μs

Ans: (A)

Sol: $\large A = A_0 (\frac{1}{2})^n$

$\large \frac{A}{A_0} = (\frac{1}{2})^n$

$\large \frac{1}{16} = (\frac{1}{2})^n$

n = 4

$\large t = n \times t_{1/2} = 4 \times 100 \mu s$

= 400 μs