Protons and neutrons like electrons are spin particles The

Protons and neutrons, like electrons, are spin ½ particles. The nuclei of ordinary helium atoms, 42He contains two protons and two neutrons each; the nuclei of another type of helium atom, 32He , contains two protons and one neutron each. The properties of liquid helium 42He and liquid helium 32He are different because one type of helium atom obeys the exclusion principle but the other doesn’t. Which is which, and why?

Solution

42He does not obey Pauli\'s Exclusion principle.

42 He is a boson. The ground state electron configuration is 1s2 , and thus has no
net angular momentum or spin. The nucleus contains 2 protons and 2 neutrons, and has a shell structure similar to that of the electrons. Thus, there is no net angular momentum or spin in the nucleus as well.
With zero spin, a 42He atom is a boson and does not obey the Pauli-Exclusion
principle.

Now consider 32He , which is an isotope of helium with one less neutron.
Although the electron configuration is the same as ordinary helium, a neutron is unpaired
in spin. The entire atom thus has spin 1/2, and is a fermion. It must obey the Pauli-
Exclusion principle.