Structure of Atom - Bohr's Model of Atom

Bohr's model is based on the quantization of energy. He proposed that electrons revolve around the nucleus in specific circular paths called 'orbits' or 'stationary states' without radiating energy. These orbits are associated with a fixed amount of energy and are designated by the principal quantum number $n = 1, 2, 3, \dots$ (or $K, L, M, N$ shells).

The angular momentum of an electron in a given orbit is quantized. An electron can revolve only in those orbits for which its angular momentum is an integral multiple of $\frac{h}{2\pi}$. This is expressed as $mvr = \frac{nh}{2\pi}$, where $m$ is the mass, $v$ is the velocity, and $r$ is the radius of the orbit.

Energy is emitted or absorbed only when an electron jumps from one stationary state to another. Energy is absorbed ($+\Delta E$) when jumping to a higher level ($n_{lower} \to n_{higher}$) and emitted ($-\Delta E$) when falling to a lower level ($n_{higher} \to n_{lower}$).

The energy difference between two levels is given by $\Delta E = E_2 - E_1 = h\nu$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \text{ J s}$) and $\nu$ is the frequency of the radiation.

Bohr's theory successfully explains the line spectrum of Hydrogen and Hydrogen-like species (ions with only one electron like $He^+$, $Li^{2+}$, and $Be^{3+}$).