Question

The half life of a radioactive element is 72 hours. in how many days will the radioactivity fall to 1/32th of its original value?

Answer 1

It will require 5 half lives,
That is 72×5= 360 hours= 15 days.

Answer 2

Answer: 15 days

Explanation: Radioactive decay follows first order kinetics.

Half-life of radioactive element = 72 hours

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{72}=9.6\times 10^{-3}hours^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t =$\frac{1}{32}\times N_0$

$N_0$ = initial amount

$\lambda$ = rate constant

t= time

$\frac{1}{32}\times N_0=N_0\times e^{-9.6\times 10^{-3}hours^{-1}\times t}$

$t=360hours=\frac{360}{24}days=15days$   (1 day=24 hours)