**Unformatted text preview: **L 2 = hcλ 8( mc 2 ) ( 4 2-3 2 ) = 0 . 9406 nm 2 , and L = 0.97 nm . (3) Q8B.8 Electrons are spin-½ fermions, so according to the Pauli Exclusion Principle only two electrons (with spins anti-aligned) can occupy each level. Thus, if we put 10 electrons into the box, the ﬁrst 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 diﬀerent: 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...

View
Full Document