Thank you for reporting, we will resolve it shortly
Q.
Half life of radioactive element is 12.5 Hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm : -
AIPMTAIPMT 2001
Solution:
The mass of radioactive substance remained is, $M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}$
Here, $M=1\,g,\,\,{{M}_{0}}=256\,g,\,{{t}_{1/2}}=12.5\,h$
$So,1=256\,{{\left( \frac{1}{2} \right)}^{n}}$
OR $\frac{1}{256}={{\left( \frac{1}{2} \right)}^{n}}$
OR ${{\left( \frac{1}{2} \right)}^{8}}={{\left( \frac{1}{2} \right)}^{N}}$
Comparing the powers on both the sides, we get
$n=8=\frac{t}{{{T}_{1/2}}}$
$\therefore t=8{{T}_{1/2}}=8\times 12.5=100\,h$