# Where does the energy come from to cause electronic transitions?

May 25, 2017

From lasers, monochromatic light... generally focused light with one wavelength is best.

Just shine a powerful laser onto a sample of atoms. A certain fraction of the population will get excited to the appropriate electronic state above the ground state with an energy difference equal to that of the incoming light.

Basically, laser comes in, gives electron energy, electron moves to higher energy level, then as it drops back down it emits a photon of that energy difference.

(For instance, a green laser example is the Nd:YAG laser using a wavelength of 532 nm.)

The excitation and relaxation are under the restrictions that:

• The energy change is quantized.
• The change in the angular momentum quantum number $l$ for all affected electrons sum up to be exactly $1$.

Hence, $2 p \to 3 s$ is appropriate, $2 p \to 3 d$ is okay, $2 p \to 3 d \to 4 p$ is good, but $2 p \to 3 p$ is forbidden.

So, in the above diagram, basically, the diagonal transitions are allowed, but the vertical transitions are not. As we noted above:

• One of the forbidden transitions is $2 p \to 3 p$, since $l$ does not change, though the change in energy is quantized by $n$.
• Each transition also changes to an adjacent column, which means $l$ changed by $1$.