- #1

Saptarshi Sarkar

- 99

- 13

- Homework Statement
- 5 non-interacting electrons are placed in an infinite potential well of width a at T=0K. Calculate the maximum energy of the system.

- Relevant Equations
- ##E_n = \frac {n^2\pi^2\hbar^2} {2ma^2}##

As the temperature given was 0K, I calculated the ground state energy of the system. I considered 2 electrons to be in the n=1 state, 2 in the n=2 state and 1 in the n=3 state by Pauli's exclusion principle.

By this configuration, I got the total energy of the system in the ground state to be

##E_{total} = 2\frac {1^2\pi^2\hbar^2} {2ma^2} + 2\frac {2^2\pi^2\hbar^2} {2ma^2} + \frac {3^2\pi^2\hbar^2} {2ma^2} = \frac {19\pi^2\hbar^2} {2ma^2}##

But, this doesn't match with any of the options provided in the question. What did I do wrong?

By this configuration, I got the total energy of the system in the ground state to be

##E_{total} = 2\frac {1^2\pi^2\hbar^2} {2ma^2} + 2\frac {2^2\pi^2\hbar^2} {2ma^2} + \frac {3^2\pi^2\hbar^2} {2ma^2} = \frac {19\pi^2\hbar^2} {2ma^2}##

But, this doesn't match with any of the options provided in the question. What did I do wrong?