Question

Ten grams of ${}^{60}Co$ kept in an open container $\beta$ decays with a half-life of 270 days. The decay products are constantly flushed out. The weight of the material inside the container after 540 days will be very nearly:

• A. 10 g
• B. 5 g
• C. 2.5 g
• D. 1.25 g

Answer 1

The correct option is C 2.5 g

The half-life $t_{\frac{1}{2}}$, by definition, is the period of time after which the sample size (number ) becomes half. For ${}^{60}Co$, since $t_{\frac{1}{2}}=270$ days, after 270 days, there will be only half the nuclei left after the $\beta$ decay, and the sample will weigh only 5 g, since you started off with 10 g. So now your sample weighs 5 g, and contains that many nuclei.
After another period of 270 days, half of that will remain, i.e. only 2.5 g. Therefore, after two half-lives, or 540 days, the sample will weigh only 2.5g.
Generally, if you have $N_0$ nuclei in the sample at present, only $\frac{N_0}{2^n}$ will remain after n half-life periods, or at $t=n\times t_{\frac{1}{2}},N=\frac{N_0}{2^n}$Think about it.