(adsbygoogle = window.adsbygoogle || []).push({}); 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 h^{2}/ 8mL_{2}?

2. Relevant equations

Energy of a single electron in state n is n^{2}h^{2}/ 8mL^{2}

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ground state of 7 electrons in infinite square well

**Physics Forums | Science Articles, Homework Help, Discussion**