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

In summary, the problem involves an electron trapped in an infinite square-well potential with a width of 0.5 nm. The initial state is n=4 and the question is asking for the possible photon energies emitted as the electron jumps to the ground state. The equations used are ΔE=13.6(1/nf2-1/ni2) and En=hbar2n2∏2/(2mL2). It is possible for the electron to transition directly from n=4 to n=1, but there may be other possible transitions as well.
  • #1
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=hbar2n22/(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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  • #2
This (4->1) is one possible transition but not the only one. The electron does not have to go "straight" from 4 to 1.
 

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

1. How does an electron jump from the n=4 state to the ground state in an infinite square well?

The electron jumps from the n=4 state to the ground state in an infinite square well due to quantum mechanical principles. The electron is confined to the well and can only exist at certain energy levels, or quantum states. When the electron absorbs or releases energy, it can transition between these energy levels, resulting in a jump from n=4 to the ground state.

2. What factors determine the energy of the electron in the n=4 state?

The energy of the electron in the n=4 state is determined by the size and depth of the infinite square well, as well as the mass of the electron. The larger the well and the lower the electron's mass, the lower its energy in the n=4 state will be.

3. Does the electron's jump from n=4 to the ground state violate the conservation of energy?

No, the electron's jump from n=4 to the ground state does not violate the conservation of energy. While the energy of the electron decreases, the energy is released in the form of a photon or other form of radiation, balancing out the energy conservation equation.

4. Can the electron jump from n=4 to the ground state be observed in a real physical system?

In theory, yes. In practice, it is difficult to create an infinite square well with perfectly confined boundaries and a single electron. However, similar energy transitions and jumps can be observed in quantum systems, such as in atoms and molecules.

5. What is the significance of the electron jumping from n=4 to the ground state in an infinite square well?

The electron's jump from n=4 to the ground state is significant because it demonstrates the quantization of energy in quantum systems. It also highlights the important role of energy transitions in understanding the behavior and properties of quantum particles.

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