The Problem Bohr Solved
Before Bohr, the atom was a puzzle. Rutherford had shown that atoms have a tiny, dense nucleus with electrons orbiting around it — like a miniature solar system. But there was a fatal flaw in that picture.
Classical physics said an accelerating charged particle must radiate energy. An electron orbiting a nucleus is constantly accelerating (changing direction), so it should continuously lose energy, spiral into the nucleus, and collapse. That doesn't happen. Atoms are stable. Also, atoms emit light only at specific, discrete wavelengths — not a continuous rainbow. The solar-system model couldn't explain either fact.
Bohr needed a new idea. He kept the planetary picture but added rules that broke from classical physics — rules that matched what experiments actually showed.
The Core Intuition
Think of an electron like a marble rolling on a staircase, not a ramp. On a ramp, the marble can stop at any height. On a staircase, it can only rest on the steps — never in between. Bohr said electrons can only occupy certain allowed "steps" (orbits) around the nucleus. While on a step, the electron does not radiate energy. It only emits or absorbs light when it jumps from one step to another, and the light's colour (wavelength) corresponds exactly to the energy difference between the steps.
This is why atomic spectra show sharp lines: each line is a jump between two specific steps.
The Precise Postulates
Bohr's model rests on three postulates, stated clearly:
Bohr's Postulates
- Stationary orbits: Electrons revolve around the nucleus only in certain fixed circular orbits without radiating energy. These are called stationary states.
- Quantized angular momentum: The angular momentum L of the electron in these orbits is an integer multiple of 2πh:
L=mvr=n2πh,n=1,2,3,…
where h is Planck's constant, m is electron mass, v is orbital speed, r is orbit radius, and n is the principal quantum number.
- Quantum jumps: An electron can jump from one stationary orbit to another by absorbing or emitting a photon whose energy equals the difference in energy between the two orbits:
Ef−Ei=hν
where ν is the photon's frequency.
What the Model Predicts
From these postulates, Bohr derived explicit formulas. For a hydrogen-like atom (one electron, nuclear charge Ze):
Radius of the nth orbit:
rn=πme2Zn2h2ε0=Zn2a0
where a0=0.529A˚ is the Bohr radius (the smallest orbit, for n=1 in hydrogen).
Energy of the nth orbit:
En=−8ε02h2n2me4Z2=−n213.6eV⋅Z2
The negative sign means the electron is bound to the nucleus. The ground state (n=1) has energy −13.6eV for hydrogen.
Wavelength of emitted light when an electron jumps from ni to nf (ni>nf):
λ1=RZ2(nf21−ni21)
where R=8ε02h3cme4≈1.097×107m−1 is the Rydberg constant. …