How Do Electron Transitions Correspond to Energy Levels in Quantum Wells?

[sss1]

Homework Statement

Can someone check whether I've done the problems in the pictures properly? not sure if i've done them correctly.

Relevant Equations

n^2h^2/8(m_e)a^2

For the problem with the diagram, I'm getting from n=4 to n=2, n=5 to n=4, n=5 to n=1 and n=4 to n=1. n=4 to n=2 corresponds to n=1 to n=2 in well C; n=5 to n=4 corresponds to n=1 to n=2 in well D; n=5 to n=1 corresponds to n=1 to n=3 in well D and n=4 to n=1 corresponds to n=1 to n=2 in well E.
For the second problem, since the node separation is given by L/n where n is the state, and given that there is no nodes between 60pm and 80pm, i worked out that n=10. So the difference in energy is (10^2-9^2)h^2/(8(m_e)(300pm))?

 

[DrClaude]

For the problem with the diagram, I'm getting from n=4 to n=2, n=5 to n=4, n=5 to n=1 and n=4 to n=1. n=4 to n=2 corresponds to n=1 to n=2 in well C; n=5 to n=4 corresponds to n=1 to n=2 in well D; n=5 to n=1 corresponds to n=1 to n=3 in well D and n=4 to n=1 corresponds to n=1 to n=2 in well E.
For the second problem, since the node separation is given by L/n where n is the state, and given that there is no nodes between 60pm and 80pm, i worked out that n=10. So the difference in energy is (10^2-9^2)h^2/(8(m_e)(300pm))?

That appears correct, except the denominator in the energy at the end.

 

[sss1]

That appears correct, except the denominator in the energy at the end.

Needs squaring?

 

[DrClaude]

Needs squaring?

Yes, and why 300 pm?

 

[sss1]

Yes, and why 300 pm?

Oh right, misread it. 200pm?

 

[DrClaude]

Oh right, misread it. 200pm?

Yes