So far, we have seen that an electron may exist in the form of various orbitals. A key concept for understanding semiconductor physics, is understanding the allowed energy values for an electron.

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.

Coulomb Force

The attraction force between the electron and proton is governed by the Coulomb 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 Potential Energy

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.

If we define the potential to be zero at infinity, the potential energy can be calculated as \[E_p = {-q^2 \over4 \pi \epsilon_0 r}\]

Total Energy of Electron

The classical model assumed that the electron revolves around the proton, giving rise to a kinetic energy defined by \[E_k = {1 \over 2} m v ^2\]

Absorption of Energy

If a photon is shined on a hydrogen atom, the electron may absorb its energy. With the classical model, any photon can be absorbed.

Observed Transition

However, the experiments show only photos with particular wavelength (hence energy) are absorbed.

Can you find which photon energies are absorbed?

Unstable orbitals

Moreover, a hydrogen atom in an excited state would can emit a photon and lose energy.

What photon energies are emitted?

Orbitals and Energy

Can you excited the electron to the 3rd energy level by shining the right photons?