Question

The half life of Uranium - $233$ is $160000$ years i.e., Uranium $233$ decays at a constant rate in such a way that it reduces to $50\%$ in $160000$ years. in how many years will it reduce to $25\%$?

• A. $80000$ years
• B. $240000$ years
• C. $320000$ years
• D. $40000$ years

Answer 1

Answer: (C)

$320000$ years

The half life of $U_{233}$ $=160000$ yrs.

$\therefore$ It becomes $50\%$ of the original amount in $160000$ yrs.

Now $25\%=$ $\frac{1}{2}\times$ $50\%$.

i.e Another half life is needed to reduce the original amount into $25\%$.

So, another $160000$ yrs. will reduce the original amount into $25\%$.

$\therefore$ The required total number of years

$=160000+160000=320000$.

i.e $320000$ yrs