Emission and Absorption: the Relation ΔE = hf

The link between levels and colors

We now have the two pieces: atoms have quantized energy levels, and light is made of photons of energy E = hf. It remains to connect them. This is the transition mechanism.

A transition = a jump between two levels

An atom can change level, but never stop between two: it jumps from one permitted level to another. This jump is always accompanied by an exchange of energy with a photon, in one direction or the other.

Absorption: the atom goes up

If a photon of energy exactly equal to the gap between two levels arrives, the atom can absorb it and rise to the higher level. The photon disappears.

   AVANT              APRES
   ---- n=2           ---- n=2  <-- electron monte
                                    ^
    photon hf                       |  absorption
      ~~~>                          |
   -O-- n=1           ---- n=1
   (electron en bas)

   condition :  hf = E2 - E1

Emission: the atom goes down

Conversely, an atom in an excited state is unstable: it falls back to a lower level by emitting a photon that carries away exactly the energy lost.

   AVANT              APRES
   -O-- n=2           ---- n=2
   (electron excite)
                                    photon hf
    descente          ---- n=1  --> ~~~>  emis
   ---- n=1           -O-- n=1

   condition :  hf = E2 - E1  (meme ecart -> meme couleur)

The fundamental relation

In both cases, the energy of the photon is imposed by the gap between the two levels:

   |ΔE| = E(haut) - E(bas) = h × f = h × c / λ

This is the key to everything:

• The atom can only exchange energies equal to the gaps between its levels.
• Each gap therefore corresponds to one frequency, and thus one very specific color.
• Since the levels are unique to each element, the emitted colors are too.

This is why an atom emits only lines, and why they are always the same. The positions of the lines in the spectrum are the direct translation of the level diagram.

Emission and absorption: the same lines

We also understand why the absorption lines coincide with the emission lines: it is the same gap ΔE that governs both, once in the direction of rising, once in that of falling. The transition n=1 -> n=2 absorbs exactly the photon that the transition n=2 -> n=1 would emit.

In summary

An atom changes level only by jumps, absorbing (rising) or emitting (falling) a photon whose energy equals exactly the gap between the two levels: |ΔE| = hf = hc/λ. Since the gaps are quantized and unique to each element, each atom exchanges only a specific set of colors — its spectral lines.