Bohr Model of Hydrogen — Core Principles

Core Principles

The Bohr model of the hydrogen atom, proposed by Niels Bohr in 1913, addressed the shortcomings of Rutherford's model by introducing quantum concepts. Its core postulates are: 1) Electrons revolve in specific, stable 'stationary orbits' without radiating energy, each with a definite quantized energy.

2) The angular momentum of an electron in these orbits is quantized, $mvr = n\frac{h}{2pi}$, where $n$ is the principal quantum number. 3) Electrons emit or absorb energy only when transitioning between these allowed orbits, with the energy of the photon equal to the energy difference between the states ($h u = E_i - E_f$).

This model successfully derived the radius ($r_n propto n^2/Z$), velocity ($v_n propto Z/n$), and energy ($E_n propto -Z^2/n^2$) of electrons in hydrogen-like atoms. It also explained the discrete line spectra of hydrogen, leading to the Rydberg formula for spectral series like Lyman (to $n=1$), Balmer (to $n=2$), Paschen (to $n=3$), etc.

While groundbreaking, it failed for multi-electron atoms and couldn't explain fine structure or the Zeeman effect, paving the way for modern quantum mechanics.

Important Differences

vs Rutherford's Atomic Model

Aspect	This Topic	Rutherford's Atomic Model
Electron Orbits	Electrons orbit the nucleus like planets around the sun, with no restrictions on orbits.	Electrons can only exist in specific, discrete 'stationary orbits' with quantized energy levels.
Atomic Stability	Predicted that atoms should be unstable (electrons radiate energy and spiral into the nucleus).	Postulated that electrons in stationary orbits do not radiate energy, thus explaining atomic stability.
Nature of Spectra	Predicted a continuous spectrum of emitted radiation.	Successfully explained the discrete line spectra of hydrogen by energy transitions between quantized levels.
Angular Momentum	No quantization of angular momentum.	Angular momentum is quantized: $mvr = nrac{h}{2pi}$.
Foundation	Based purely on classical mechanics and electromagnetism.	Incorporated quantum concepts (Planck's quantum hypothesis) into classical mechanics.
Successes	Explained alpha-particle scattering and the existence of a dense, positive nucleus.	Explained hydrogen spectrum, atomic stability, and calculated energy levels, radii, and velocities for hydrogen-like atoms.

The Rutherford model, while correctly identifying the nuclear structure, failed to explain atomic stability and discrete spectra based on classical physics. The Bohr model, building upon Rutherford's foundation, introduced revolutionary quantum postulates – stationary orbits, quantized angular momentum, and energy transitions – to successfully account for these phenomena, particularly for hydrogen. It marked a crucial departure from classical physics towards quantum mechanics, providing a framework to understand atomic energy levels and spectral lines.