The Bohr Model and Energy Levels

The problem of the classical atom

In the classical model, the electron orbits the nucleus like a planet around the Sun. But a moving charge should radiate energy continuously, slow down, and crash into the nucleus within a fraction of a second. According to classical physics, no atom should be stable. Yet they are. There is a major contradiction here.

Bohr's idea (1913): permitted and forbidden orbits

Niels Bohr proposes a break: the electron can occupy only certain very specific orbits, called stationary orbits, on which it does not radiate. Between these orbits, nothing: the others are forbidden.

              noyau
                (+)      <- orbites permises uniquement
              .  |  .
            .    |    .
          (   .--+--.   )   n=1  (la plus proche, la plus liee)
          (  .  (+)  .  )   n=2
          ( .         . )   n=3
           .           .
            .         .

To each permitted orbit corresponds a well-defined energy. The energy of the atom can therefore take only discrete values: we say it is quantized. These values are the energy levels.

The energy-level diagram

These permitted energies are represented by a level diagram: a ladder in which each rung is an allowed energy. By convention, the energies are negative (the electron is bound, energy would have to be supplied to tear it away) and they crowd together toward the top:

   E (eV)
     0  -------------------------  (electron libre : ionise)
                                    ^
   -0,85 --------------------  n=4  |  niveaux
   -1,51 --------------------  n=3  |  de plus en plus
                                    |  serres
   -3,40 --------------------  n=2  |
                                    |
                                    |
   -13,6 --------------------  n=1  (etat fondamental : le plus bas, le plus stable)

Ground state and excited states

• The lowest level (n=1) is the ground state: the most stable, the one the atom naturally finds itself in.
• The higher levels (n=2, 3, ...) are the excited states: unstable, the atom stays there only for an instant.
• The level E = 0 corresponds to the electron being torn away: the atom is ionized. The energy needed to go from n=1 to E=0 is the ionization energy (13,6 eV for hydrogen).

What the model finally explains

This quantization solves both mysteries at once:

1. The stability of the atom: on its lowest permitted orbit, the electron cannot go any lower or radiate. It does not crash.
2. Line spectra: since only certain energies exist, the atom can exchange only certain precise amounts of energy — and therefore emit only certain colors. This is the subject of the next chapter.

Note: the Bohr model is outdated (modern quantum mechanics replaces the orbits with probability "clouds"). But its central idea — the quantization of energy — remains perfectly correct.

In summary

Bohr postulates that the electron can occupy only permitted orbits, with quantized energies (the energy levels), represented on a diagram of negative rungs. The lowest is the ground state, the others are excited, and E=0 marks ionization. This model explains both why the atom is stable and why it emits only lines.