The Problem with the Rutherford Model
By 1911, Rutherford's gold foil experiment had revealed that atoms have a small, dense, positively charged nucleus with electrons orbiting around it , much like planets around the Sun. It was a compelling picture, but it had a fatal flaw.
According to classical electromagnetism, any charged particle undergoing circular motion is accelerating. An accelerating charge must emit electromagnetic radiation, losing energy in the process. If electrons obeyed this rule, they would spiral inward and crash into the nucleus in roughly seconds. Atoms simply would not exist in a stable form.
Clearly, something beyond classical physics was needed.
Imagine a satellite orbiting Earth that constantly loses altitude due to atmospheric drag, eventually burning up on re-entry. Classical physics predicted electrons would do exactly this , but of course, matter around us is stable, so the classical picture must be wrong.
Bohr's Revolutionary Postulates
In 1913, Niels Bohr proposed a radical set of rules , his postulates , to fix the Rutherford model:
-
Electrons occupy stable, non-radiating orbits. In these special orbits, the usual rules of classical electromagnetism are suspended. An electron in such an orbit does not emit radiation, no matter how long it stays there.
-
Angular momentum is quantised. An electron can only occupy orbits where its angular momentum is an integer multiple of :
where:
- = mass of the electron ( kg)
- = orbital speed of the electron
- = orbital radius
- = quantum number (a positive integer)
- = Planck's constant ( J s)
- Energy is emitted or absorbed only when an electron jumps between orbits. The energy of the emitted or absorbed photon equals the difference in energy between the two levels.
Quantisation: The restriction of a physical quantity (such as angular momentum or energy) to only certain discrete, specific values , rather than any value across a continuous range.
The quantity appears so frequently in quantum physics that it has its own symbol: ("h-bar"), called the reduced Planck constant. So Bohr's condition is often written .