An electron is trapped in an infinite square-well potential of width 0.2 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.)

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Explanation:

The energies in a infinite square-well potential of width a is given by

where me=9.1*10^{-31}kg, hbar=1.05*10^{-34}Js and a= 0.2*10^{-9}m.

From the state n=4 the electron can pass to state n=3, n=2 and n=1. The different transitions can be

n4->n3=E4-E3

n3->n2=E3-E2

n2->n1=E2-E1

Hence, by replacing we have that the photon energies emitted are given by

However, the transitions T4-2, T4-3, T3-1 are also allowed

hope this helps!!

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double the distance = divide strength by 4