Ten grams of ^ 57 Co is placed in an open container and undergoes...

In $\beta$-decay, the mass number of the nucleus remains unchanged. The parent nucleus ^{57}\text{Co}$decays into a daughter nucleus which is also a solid and remains in the open container.<br><br>The mass of the emitted$\beta$-particles and the mass equivalent of the energy released are negligible compared to the total mass of the material. Thus, the atomic mass of the daughter nucleus is approximately equal to that of the parent nucleus.<br><br>After$540 \text{ days}$(which corresponds to exactly two half-lives, since$T_{1/2} = 270 \text{ days}$), the mass of ^{57}\text{Co}$ remaining is $10 \times \left(\dfrac{1}{2}\right)^2 = 2.5 \text{ g}$.

The mass of the daughter nucleus formed is $10 - 2.5 = 7.5 \text{ g}$.

Since both the parent and daughter nuclei are solid and present in the container, the total weight of the material inside the container remains approximately $2.5 + 7.5 = 10 \text{ g}$.