Bohr's Model — Definition

Definition

Imagine a tiny solar system, but with a twist! Before Niels Bohr, scientists like Rutherford proposed that atoms had a central nucleus with electrons orbiting around it, much like planets around the sun.

However, this 'planetary model' had a big problem: according to classical physics, an electron moving in a circle should continuously lose energy by radiating electromagnetic waves. If it lost energy, it would spiral inwards and eventually crash into the nucleus, making atoms unstable.

But we know atoms are stable! Also, when atoms are excited, they emit light only at specific, discrete wavelengths, forming a 'line spectrum,' not a continuous rainbow like classical physics would predict from a spiraling electron.

Niels Bohr, in 1913, came up with a brilliant solution by combining classical physics with the emerging idea of quantum mechanics (specifically, Planck's quantum theory). He proposed a model for the hydrogen atom (and hydrogen-like species) based on three revolutionary postulates:

1
Stationary Orbits: — Electrons can only revolve around the nucleus in certain specific, stable circular orbits, called 'stationary states,' without radiating energy. This was a direct contradiction to classical electromagnetism.
2
Quantization of Angular Momentum: — In these stable orbits, the angular momentum of the electron is quantized. This means it can only take on discrete values that are integral multiples of $rac{h}{2pi}$, where $h$ is Planck's constant. So, $mvr = n\frac{h}{2pi}$, where $n$ is an integer (1, 2, 3, ...), called the principal quantum number.
3
Energy Transitions: — An electron can jump from one stationary orbit to another. When it jumps from a higher energy orbit to a lower energy orbit, it emits a photon of light. Conversely, to jump from a lower energy orbit to a higher energy orbit, it must absorb a photon. The energy of this emitted or absorbed photon is exactly equal to the energy difference between the two orbits: $Delta E = E_{final} - E_{initial} = h

u$, where$ u$ is the frequency of the photon.

Bohr's model successfully explained the stability of the hydrogen atom and, crucially, accurately predicted the wavelengths of the spectral lines observed in the hydrogen emission spectrum. It introduced the idea that energy within an atom is not continuous but exists in discrete 'packets' or 'quanta,' a fundamental concept in quantum chemistry and physics.

While revolutionary, it had limitations, particularly for multi-electron atoms, but it was a monumental step forward in understanding atomic structure.