Beyond the Bohr orbits

From the Bohr model to probability clouds

The Bohr model and its limits

The Bohr model pictured the electron traveling along well-defined orbits around the nucleus, like planets. It already explained the energy levels and the spectra of hydrogen — an immense advance. But it kept a false classical image: that of an electron having, at every instant, a precise position and velocity tracing a sharp trajectory.

Yet we now know this is impossible: the uncertainty principle forbids knowing both position and velocity at once. The notion of a well-traced orbit no longer makes sense.

   Modele de Bohr (faux) :          Modele quantique (juste) :

        (+)                              . : ' . :. '
       /   \\   orbite nette            : .(+): . .' :   nuage flou
      | (+) |  <- l'electron            ' :. ' . : .'    (probabilite
       \\   /      "est ici"             . ' . :. ' .'     de presence)
        ---
   trajectoire precise              PAS de trajectoire

The orbital: a probability cloud

Quantum mechanics replaces the orbit with the orbital. An orbital is not a path: it is a region of space where the electron has a high probability of being found. It is described by the wave function ψ, whose square |ψ|^2 gives the probability density of presence at each point.

   |ψ|^2 grand  ->  forte chance de trouver l'electron ici (nuage dense)
   |ψ|^2 petit  ->  faible chance (nuage tenu)

The orbital is often represented by the volume that contains, say, 90 % of the probability of presence: this is the "shape" of the orbital.

The electron is "everywhere at once"... until measurement

As long as it is not measured, the electron is not "somewhere" on an orbit: it is delocalized, spread throughout the cloud according to |ψ|^2, somewhat like a standing wave fills an entire vibrating string. It is only by measuring its position that we "find" it at a precise point — and the cloud was merely the map of the probabilities of that result.

   Analogie : une corde de guitare qui vibre
        la vibration occupe TOUTE la corde a la fois
        -> l'electron "occupe" toute son orbitale a la fois

What Bohr got right, and what needs correcting

   Bohr avait RAISON sur :   les niveaux d'energie quantifies,
                             les transitions et les spectres

   Bohr avait TORT sur :     l'orbite/trajectoire precise
                             -> remplacee par l'orbitale (nuage de proba)

The modern model keeps the quantization of energy (the great achievement) but abandons the image of the trajectory (the classical error). It is a refinement, not a total rejection.

In summary