Bohr's Model — Core Principles

Core Principles

Bohr's model, proposed in 1913, revolutionized atomic theory by introducing quantum concepts to explain atomic stability and line spectra. It addressed the failures of Rutherford's model by postulating that electrons orbit the nucleus in specific, non-radiating 'stationary states' with quantized energy.

The key tenets include: (1) Electrons exist in discrete orbits without energy loss. (2) Angular momentum of an electron in these orbits is quantized, $mvr = n\frac{h}{2pi}$. (3) Energy is absorbed or emitted only when an electron transitions between these discrete energy levels, with the photon energy $Delta E = h u$.

This model successfully derived formulas for the radius ($r_n = 0.529 \frac{n^2}{Z} \text{ Å}$), velocity ($v_n = 2.18 \times 10^6 \frac{Z}{n} \text{ m/s}$), and energy ($E_n = -13.6 \frac{Z^2}{n^2} \text{ eV}$) of electrons in hydrogen and hydrogen-like atoms.

It also accurately predicted the hydrogen spectrum using the Rydberg formula. While foundational, it failed for multi-electron atoms and couldn't explain phenomena like the Zeeman effect, paving the way for more advanced quantum mechanics.

Important Differences

vs Rutherford's Model

Aspect	This Topic	Rutherford's Model
Electron Orbits	Electrons orbit the nucleus like planets around the sun, with no restriction on orbit radius or energy.	Electrons orbit only in specific, discrete 'stationary orbits' with quantized radii and energy levels.
Atomic Stability	Predicts that electrons should continuously radiate energy and spiral into the nucleus, making atoms unstable (classical physics failure).	Postulates that electrons do not radiate energy in stationary orbits, thus explaining atomic stability (quantum postulate).
Atomic Spectra	Predicts a continuous spectrum of light if electrons were to spiral inwards.	Successfully explains the discrete line spectrum of hydrogen by postulating energy transitions between quantized levels.
Angular Momentum	No quantization of angular momentum; any value is possible.	Angular momentum is quantized, $mvr = nrac{h}{2pi}$.
Applicability	Could not explain atomic stability or line spectra for any atom.	Successfully explained hydrogen and hydrogen-like ions, but failed for multi-electron atoms.

Rutherford's model, while correctly identifying the nuclear structure, failed to explain atomic stability and the observed line spectra based on classical physics. Bohr's model, by introducing quantum postulates like stationary orbits and quantized angular momentum, successfully resolved these issues for hydrogen-like atoms. It moved atomic theory from a purely classical framework to one incorporating quantum principles, marking a significant conceptual leap. The key difference lies in the quantization of energy and angular momentum, which was absent in Rutherford's purely classical approach.