Question

The half-life of $Bi^{210}$is 5 days. What time is taken by (7/8)^th part of the sample to decay.

• A. 3.4 days
• B. 10 days
• C. 15 days
• D. 20 days

Answer 1

Answer: (C)

15 days

Answer 2

By using$N = N_{0}\left( \frac{1}{2} \right)^{t/T};$

where $N = \left( 1 - \frac{7}{8} \right)N_{0} = \frac{1}{8}N_{0}$

So $\frac{1}{8}N_{0} = N_{0}\left( \frac{1}{2} \right)^{t/T}$⇒$\left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{t/5}$

⇒ t =15 days .