This is a Physical Chemistry Problem: For a particle in a cubic box of length a,...

This is a Physical Chemistry Problem: For a particle in a cubic box of length a, how many states have energy in the range of 0 to 16(h²/8ma²)?

Expert Solution

E = (nx ² + ny ² + nz ² ) h2 /(8ma2 ).

Rearranging gives E (8ma² )/ h² = (nx ² + ny ² + nz ² )

nx, ny, nz, 1,1, 1 2,1, 1 1,2, 1 1,1, 2 1,2, 2 2,1, 2 2,2, 1 1,1, 3 1,3, 1 3,1, 1

E(8ma² )/ h² 3 6 6 6 9 9 9 11 11 11

nx, ny, nz, 2,2, 2 2,1, 3 1,2, 3 3,2, 1 2,3, 1 1,3, 2 3,1, 2 2,2, 3 2,3, 2 3,2, 2 E(8ma² )/ h² 12 14 14 14 14 14 14 17 17 17

nx, ny, nz, 1,1, 4 4,1, 1 1,4, 1 1,3, 3 3,1, 3 3,3, 1

E(8ma2 )/ h2 18 18 18 19 19 19

TOTAL: 17 states and 6 energy levels lie within this range

queen_honey_blossom answered 1 year ago

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