sabinscabin
Sep26-08, 01:11 AM
1. The problem statement, all variables and given/known data
Seven electrons are trapped in a one dimensional infinite square well of length L. What is the ground state energy of this system as a multiple of h2 / 8mL2?
2. Relevant equations
Energy of a single electron in state n is n2h2 / 8mL2
3. The attempt at a solution
Pauli exclusion principle says all 7 must have different quantum numbers.
starting from n = 1, we have L = 0 and mL = 0, and ms = -1/2 and 1/2, so there are two electrons in n = 1.
For n = 2, we have two electrons for L = 0
for L = 1, we have mL = -1, 0, 1, which means this subshell can hold 6 electrons. The remaining 3 electrons go into this subshell then.
Final tally: 2 electrons for n = 1 and 5 electrons for n = 2.
Total energy as a multiple of the given term then = 2*1^2 + 5*2^2 = 22.
Halliday Resnick says 44 for some reason. Can anybody spot my mistake?
Seven electrons are trapped in a one dimensional infinite square well of length L. What is the ground state energy of this system as a multiple of h2 / 8mL2?
2. Relevant equations
Energy of a single electron in state n is n2h2 / 8mL2
3. The attempt at a solution
Pauli exclusion principle says all 7 must have different quantum numbers.
starting from n = 1, we have L = 0 and mL = 0, and ms = -1/2 and 1/2, so there are two electrons in n = 1.
For n = 2, we have two electrons for L = 0
for L = 1, we have mL = -1, 0, 1, which means this subshell can hold 6 electrons. The remaining 3 electrons go into this subshell then.
Final tally: 2 electrons for n = 1 and 5 electrons for n = 2.
Total energy as a multiple of the given term then = 2*1^2 + 5*2^2 = 22.
Halliday Resnick says 44 for some reason. Can anybody spot my mistake?