A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level…

Q: A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

(A) 6 h

(B) 12 h

(C) 24 h

(D) 128 h

Ans: (B)

Sol: $\large R = R_0 (\frac{1}{2})^n$ ; where n = number of half lives

$\large 1 = 64(\frac{1}{2})^n $

$\large \frac{1}{64} = (\frac{1}{2})^n $

n = 6

$\large n = \frac{t}{t_{1/2}}$

$\large t = n \times t_{1/2} = 6 \times 2$

t = 12 h