Question

If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm

• A. In 8 minutes
• B. In 12 minutes
  
• C. In 16 minutes
• D. In 20 minutes

Answer 1

The correct option is B In 12 minutes


substance reduces to 10 gm (i.e. becomes half in 4 min). So $T_{\frac{1}{2}}=4min$. Again $M=M_0{\left(\frac{1}{2}\right)}^{t/T_{1/2}}$
$\Rightarrow 10=80{\left(\frac{1}{2}\right)}^{\frac{t}{4}}\Rightarrow \frac{1}{8}={\left(\frac{1}{2}\right)}^3{\left(\frac{1}{2}\right)}^{\frac{t}{4}}\Rightarrow t=12min$.