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)

The mass of radioactive substance remained is, $M=M_0{\left(\frac{1}{2}\right)}^n$
Here, $M=1g,M_0=256g,t_{1/2}=12.5h$
$So,1=256{\left(\frac{1}{2}\right)}^n$
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
$n=8=\frac{t}{T_{1/2}}$
$\therefore t=8T_{1/2}=8\times 12.5=100h$