Question

10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to stop us imagining a spin-half boson.) What then would be the degenera- cy of the He atom's ground state? (c) What would the degeneracy be if the two electrons were some how distinguishable? (For example, they might have slightly different masses.) The different num- bers that you should get in the three parts of this problem are examples of the different statistics of fermions, bosons, and distinguishable particles. (See Chapter 13.)

Answer 1

Fermion always obay pauli exclusion So when the both election is spin then o . principle » Fermion Same state هما from pauli exclusion poinciple only two state is Possible as above. But fermions are identical and indistinguishable so the above two state is same. So total degeneracy is is one for spin ž fermion. 3 (6) Boson dont obery paule exclusion principle. But Boson are identical and indistinguishable. . T TA 1 L - 2 de (same as indistinguishable So total degeneracy is 3. for boson. (0) Distinguishabe particle obey maxwell statistic that does not obey pauli exclusion poinciple. In - tu 1 2 total u state possible for distinguishable particle total degeneracy y. LJ