Question

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 : -

• A. 50 Hrs
• B. 100 Hrs
• C. 150 Hrs
• D. 200 Hrs

Answer 1

Answer: (B)

100 Hrs

Answer 2

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
$n=8=\frac{t}{{{T}_{1/2}}}$
$\therefore t=8{{T}_{1/2}}=8\times 12.5=100\,h$