The nuclide is “doubly magic” in that both its proton number and its neutron number represent filled nucleon shells. An additional proton would yield and an additional neutron would yield . These “extra” nucleons should be easier to remove than a proton or a neutron from the filled shells of .

(a) We have to calculate the energy required to move the “extra” proton from and compare it with the energy required to remove a proton from the filled proton shell of .

(b) We have to calculate the energy required to remove the “extra” neutron from and compare it with the energy required to remove a neutron from the filled neutron shell of . We have to answer whether our results agree with expectation. Needed atomic mass data is given in the following table:

The masses of the proton and the neutron are 1.007276 u and 1.008665 u, respectively.

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(a)

We have to calculate the energy required to move the “extra” proton from and compare it with the energy required to remove a proton from the filled proton shell of .

The energy required to move the “extra” proton from can be calculated by considering the nuclear process

.

It will be equal to

We calculate next the energy required to remove a proton from the filled proton shell of .

It will be given by the nuclear process

.

It will be equal to

(b)

We have to calculate the energy required to remove the “extra” neutron from and compare it with the energy required to remove a neutron from the filled neutron shell of .

The energy required to remove the “extra” neutron from can be calculated from the nuclear process

.

It will be equal to

The energy required to remove a neutron from the filled neutron shell of can be calculated from the nuclear process

.

It will be equal to

We note that our results agree with expectation that because the nuclide is “doubly magic” in that both its proton number and its neutron number represent filled nucleon shells, protons are more tightly bound in it than in the nuclide, and that neutrons are more tightly bound in it than in the nuclide .