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Unformatted text preview: L 2 = hc 8( mc 2 ) ( 4 23 2 ) = 0 . 9406 nm 2 , and L = 0.97 nm . (3) Q8B.8 Electrons are spin fermions, so according to the Pauli Exclusion Principle only two electrons (with spins antialigned) can occupy each level. Thus, if we put 10 electrons into the box, the rst 5 levels are occupied by two electrons each, and the highest level is n = 5 . If we ignore the electrostatic repulsion, then the total energy of all 10 electrons is E total = ( hc ) 2 8( mc 2 ) L 2 ( 2 1 2 + 2 2 2 + 2 3 2 + 2 4 2 + 2 5 2 ) = 110 ( hc ) 2 8( mc 2 ) L 2 . (4) For a box of length L = 3 . 0 nm we calculate E total = 4 . 6 eV . If electrons were bosons, then the total energy would certainly be dierent: all 10 such electrons would settle into the lowest ( n = 1) energy level, and the total energy would be lower by a factor of 10/110. 1...
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 Spring '11
 EricSzarmes
 Physics, Energy, Work, Photon

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