- #1

tanaygupta2000

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- 14

- Homework Statement
- Consider eight electrons in a one dimensional box of length 'a' extending from x = 0 to x = a. What is the minimum allowed total energy using Pauli's exclusion principle for the system (m = mass of electron)?

- Relevant Equations
- Energy of particles in a 1D box = n^2 h^2/ (8mL^2)

For the given problem, I know that the quantized energy for the particles in a 1D box is given by -

E(n) = n^2 h^2/ (8mL^2)

Here m = mass of electron

L = Length of the box = a

Now, since there are 8 electrons, but only 2 can occupy one energy level,

so I used n^2 = (1)^2 + (2)^2 = 1 + 4 = 5

So for a 'pair' of electrons, E = 5h^2/8ma^2

Hence total energy should be (since there are 8 electrons) = 4 * 5h^2/8ma^2

= 5h^2/2ma^2

Is my approach correct for attempting the question ?

Please guide.

E(n) = n^2 h^2/ (8mL^2)

Here m = mass of electron

L = Length of the box = a

Now, since there are 8 electrons, but only 2 can occupy one energy level,

so I used n^2 = (1)^2 + (2)^2 = 1 + 4 = 5

So for a 'pair' of electrons, E = 5h^2/8ma^2

Hence total energy should be (since there are 8 electrons) = 4 * 5h^2/8ma^2

= 5h^2/2ma^2

Is my approach correct for attempting the question ?

Please guide.