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

Answer: (B)

In 12 minutes

Answer 2

20 gm substance reduces to 10 gm (i.e. becomes half in 4 min. So $T_{1/2} = 4\min$. Again $M = M_{0}\left( \frac{1}{2} \right)^{t/T_{1/2}}$

⇒ $10 = 80\left( \frac{1}{2} \right)^{t/4}$⇒$\frac{1}{8} = \left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{t/4}$⇒ t = 12 min.