Infinite Square Well Electron Jumps from n=4 to ground state

AI Thread Summary
An electron in an infinite square-well potential of width 0.5 nm can emit various photon energies when transitioning from the n=4 state to the ground state (n=1). The energy difference for this transition can be calculated using the equation ΔE=13.6(1/nf^2 - 1/ni^2). While the direct transition from n=4 to n=1 is one possibility, other transitions (such as n=4 to n=2 and then n=2 to n=1) can also occur, leading to different photon energies. It is essential to consider all possible transitions to fully understand the emitted photon energies. The discussion emphasizes the importance of using the correct equations to calculate energy levels in quantum mechanics.
Mrbilly
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Homework Statement


An electron is trapped in an infinite square-well potential of width 0.5 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?

Homework Equations


ΔE=13.6(1/nf2-1/ni2)
En=hbar2n2∏2/(2mL2)

The Attempt at a Solution


Im not quite sure if this is a trick or not, but I thought that I did not need the energy equation for the 1-D infinite well, En, but just needed to use the ΔE equation and do n=4->n=1. Or do I also need to find the energy at n=4 and n=1 and show those as well?
 
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This (4->1) is one possible transition but not the only one. The electron does not have to go "straight" from 4 to 1.
 
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