NESA Physics Properties of the Nucleus

Stability is determined by binding energy per nucleon, not total binding energy, so we cannot determine which nucleus is more stable without knowing their nucleon numbers.

Stability depends on binding energy per nucleon, which cannot be determined from total binding energy alone.

Binding energy is directly proportional to mass defect according to the mass-energy equivalence equation $E = \Delta m c^2$. Therefore, a greater binding energy means a greater mass defect.

Since nucleus X has a greater binding energy, it must have a greater mass defect than Y, not the other way around.

Working backwards, Lithium-7 (${}^{7}_{3}\text{Li}$) plus an alpha particle (${}^{4}_{2}\alpha$) gives an intermediate nucleus of Boron-11 (${}^{11}_{5}\text{B}$). Since this was formed by absorbing a neutron (${}^{1}_{0}\text{n}$), the original nucleus $X$ must be Boron-10 (${}^{10}_{5}\text{B}$).

If Boron-11 absorbed a neutron, it would form Boron-12. An alpha decay from Boron-12 would produce Lithium-8, not Lithium-7.

If Lithium-6 absorbed a neutron, it would form Lithium-7 directly, but the question states that Lithium-7 is produced via alpha decay after the neutron absorption.

If Lithium-10 absorbed a neutron, it would form Lithium-11. An alpha decay from Lithium-11 would produce Hydrogen-7, not Lithium-7.

This incorrect answer comes from dividing the initial mass by the half-life ($120 / 30 = 4$), rather than calculating the exponential decay over 3 half-lives.

Since 90 years is exactly 3 half-lives ($90 / 30 = 3$), the initial mass is halved 3 times. The remaining mass is $120 \text{ g} / 2^3 = 15 \text{ g}$.

This incorrect answer comes from dividing the initial mass by the number of half-lives ($120 / 3 = 40$), instead of dividing by $2^3$.

This is the mass that would remain after only 1 half-life (30 years), not the 3 half-lives (90 years) specified in the question.