Question about microstates and electrons

[Clara Chung]

Homework Statement

Attached

Relevant Equations

Attached

In 8a) I don't understand the question, does spin = 1/2 mean the magnitude of the spin or the z-component of the spin is 1/2? Can the electrons possesses be any of the spin=1/2 or -1/2? Are the electrons distinguishable?

 

[DrClaude]

Spin-1/2 refers to the spin quantum number, so the electrons are free to have their spin point along any direction. On that subject, part (d) is not well formulated: it should specify $s_z$, not just $s$.

The electrons are indistinguishable, as stated in the problem. (Generally speaking, quantum particles should always be considered indistinguishable unless specified otherwise or due to a particular physical situation, like atoms in a crystal.)