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 $\left(t_{1/2}\right)$, by definition, is the period of time after which the sample sixe (number) becomes half. For${}^{60}$Co, since $\left(t_{1/2}\right)$= 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 weights 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 weight only $\begin{array}{c}2.5g\end{array}$.
Generally, if you have $N_0$ nuclei in the sample at present, only $N_0/2^n$ will remain after n half- life periods, or at $t=n\times t_{1/2},N=N_0/2^n$Think about it.