Question

Of all atoms with atomic mass number A= 101, use the semiempircal mass formula to determine which one is stable to beta decay.

Answer 1

To identify a stable atom with atomic mass number A=101, we need an isotope with an appropriate neutron-to-proton ratio for its atomic number and one that does not exceed Z>83 to be stable against beta decay, but exact isotope values cannot be determined without specific n/p ratios.

Step-by-step explanation:

To determine which atom with atomic mass number A=101 is stable to beta decay using the semiempirical mass formula, we must look at the neutron-to-proton ratio (n/p ratio).

Atoms with an n/p ratio that is too high are prone to beta decay, where a neutron is converted to a proton, thus increasing the atomic number (Z) while keeping the mass number (A) constant.

For stability against beta decay, the nuclide should have an n/p ratio close to the value that is considered stable for its particular atomic number range.

However, specific numbers aren't provided to conclusively identify which isotope of A=101 is stable. We are also informed that nuclides with Z>83 are typically unstable due to being too heavy, usually decaying by alpha emission, and that for light elements, a high neutron-to-proton ratio indicates beta decay would occur.

Therefore, we need to find an isotope of A=101 with the most appropriate n/p ratio for its Z that is not greater than 83.

Answer 2

Based on the semiempirical mass formula, we can determine that tin-118 is stable to beta decay among the atoms with atomic mass number A=101.

Step-by-step explanation:

The semiempirical mass formula can be used to determine whether an atom is stable to beta decay based on its atomic mass number (A). For atoms with A = 101, we need to consider the neutron-to-proton ratio. Nuclei with high neutron-to-proton ratios tend to decay by converting a neutron to a proton and emitting a beta particle (electron) in the process. Therefore, the atom with a neutron-to-proton ratio close to 1.4 is more likely to undergo beta decay.

In the given options, the only atom with a neutron-to-proton ratio close to 1.4 is tin-118. Thus, tin-118 is stable to beta decay.