Q.What are the postulates of Bohr's model of hydrogen atom? Discuss the importance of this model to explain various series of line spectra in Hydrogen atom.

Bohr proposed quantised, non-radiating circular orbits for the electron; transitions between these orbits emit/absorb photons of fixed energy, which correctly explains the entire line-spectrum structure (Lyman/Balmer/Paschen/Brackett/Pfund series) of the hydrogen atom.

Postulates of Bohr's atomic model:

1. Stationary orbits: The electron in a hydrogen atom (or any hydrogen-like species) revolves around the nucleus only in certain fixed circular paths of definite energy, called stationary states or orbits. As long as it stays in a given orbit, the electron does not lose or radiate energy, despite undergoing centripetal acceleration (this defied classical electromagnetic theory, which predicts continuously radiating, spiralling electrons).

2. Quantisation of angular momentum: Only those orbits are permitted for which the angular momentum of the electron is an integral multiple of h/2π:

   mvr = nh/2π, where n = 1, 2, 3, ... (the principal quantum number), m = electron mass, v = electron speed, r = orbit radius, h = Planck's constant.

3. Energy absorption/emission on transition: Energy is emitted or absorbed by the atom only when the electron jumps from one permitted orbit to another. If the electron falls from a higher-energy orbit (n₂) to a lower-energy orbit (n₁), a photon is emitted; if it absorbs energy, it jumps to a higher orbit. The energy of the photon involved exactly equals the energy difference between the two orbits:

   ΔE = E(n₂) − E(n₁) = hν, where ν is the frequency of the radiation absorbed/emitted.

Importance in explaining the hydrogen line spectra:

Using these postulates, Bohr derived the energy of the electron in the nth orbit of hydrogen as E_n = −13.6/n² eV (or −2.18×10⁻¹⁸/n² J), and the orbit radius r_n = 0.529 n² Å.

When an electron transitions from a higher orbit n₂ to a lower orbit n₁, the emitted photon's wavenumber follows the Rydberg-type formula:

1/λ = R_H (1/n₁² − 1/n₂²)

which matched the experimentally observed hydrogen spectral lines with excellent accuracy — this was the first major triumph of the model.

Depending on which lower orbit (n₁) the electron falls into, the emitted lines group into distinct series, each named and falling in a specific region of the electromagnetic spectrum:

• Lyman series: transitions to n₁ = 1 (from n₂ = 2,3,4...) — ultraviolet region. …