So far, we have seen that an electron may exist in various states which we called them orbitals. A key concept for understanding semiconductor physics is that each orbital has a distinct energy; hence, the allowed energy levels for an electron are quantized. Here we review the concepts of kinetic and potential energies in classical physics and study the quantized energy levels of electrons in a hydrogen atom.
Once again, we look at a Hydrogen atom that consists of one electron and one proton.
These subatomic particles are equally, but oppositely, charged.
The attraction force between the electron and proton is governed by the Coulomb's law:
\[F = {q^2 \over 4 \pi \epsilon_0 r^2}\]
Here \[\epsilon_0\] is permittivity of free space, \[q\] is electron charge, and \[r\] is the distance between the particles.
The electron’s potential energy at any point in space is the work done by an external force to move the electron from the reference point to that point at a constant velocity.
To move the electron at constant velocity, we need to apply an external force that is equal but opposite to the Coulomb force.
When is the work done on the electron positive and when is negative? When is the potential energy positive and when is it negative?
If we define the potential to be zero at infinity, the potential energy can be calculated as \[E_p = {-q^2 \over4 \pi \epsilon_0 r}\]
The classical model assumed that the electron revolves around the proton, giving rise to a kinetic energy defined by \[E_k = {1 \over 2} m v ^2\]
Note that we have slowed down the electron rotation by many orders of magnitude for demonstration purposes.
If a photon is shined on a hydrogen atom, the electron may absorb its energy. With the classical model, any photon can potentially be absorbed.
However, the experiments show only photos with particular wavelengths (hence energies) are absorbed.
Can you find which photon energies are absorbed?
Each distinct energy level corresponds to an orbital, with 1S having the lowest energy level (n=1) and 2S, 2Px, 2Py,2Pz have the second lowest energy levels (n=2). For other atoms that have more than one electron, 2P orbitals have a slightly larger energy compared to 2S due to electron-electron interaction.
Moreover, a Hydrogen atom in an excited state would emit a photon and lose energy.
Photons with which energies are emitted?
Can you excited the electron to the 3rd energy level by shining the right photons?
The transition from an unstable state to a lower state is a stochastic process with an average lifetime on the order of 10-8s.