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The density for spin-1/2 fermions in a box is ?(?) = ?/ 2?^2( 2?/ℏ^2)^3/2 √? will...

The density for spin-1/2 fermions in a box is

?(?) = ?/ 2?^2( 2?/ℏ^2)^3/2 √?

will the Fermi energy increase, decrease, or stay the same if

1) we increase the number of fermions?

2) we increase the mass of the fermions?

3) we increase the spin of the fermions (say from 1/2 to 3/2)?

4) Make a rough sketch of the original density-of-states and compare to 1-3

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