Q.(i) Explain Bohr model of Hydrogen atom

Bohr fixed Rutherford's two big failures — instability and the inability to explain line spectra — by proposing quantized circular orbits in which electrons neither radiate energy nor spiral into the nucleus, only absorbing/emitting energy in discrete jumps. The photoelectric effect (electron ejection above a threshold light frequency) is a separate but related quantum phenomenon from the same NCERT unit.

(i) Bohr's model of the hydrogen atom

Niels Bohr proposed the following postulates for the hydrogen atom (and hydrogen-like species):

1. The electron in a hydrogen atom can move around the nucleus only in certain fixed circular paths of definite energy, called stationary states or orbits. As long as the electron stays in a given orbit, it does not radiate (lose) energy — this fixed the instability problem of Rutherford's model.
2. The angular momentum of the electron in an orbit is quantized: it can only take values that are integral multiples of h/2π, i.e. mvr = nh/2π, where n = 1, 2, 3, ... (the principal quantum number), m = mass of electron, v = velocity, r = radius of orbit, h = Planck's constant.
3. Energy is emitted or absorbed by the atom only when the electron jumps from one allowed orbit to another — from a lower to a higher orbit on absorbing energy, and from a higher to a lower orbit on emitting energy — and the energy of the photon involved equals the energy difference between the two orbits: ΔE = E2 − E1 = hν.
4. For the hydrogen atom, the energy of the electron in the nth orbit is En = −2.18 × 10⁻¹⁸ (Z²/n²) J, and the radius of the nth orbit is rn = 52.9 n² pm (with Z = 1 for hydrogen).

(ii) Two drawbacks of Rutherford's model

1. It could not explain the stability of the atom. According to classical electromagnetic theory, an electron revolving in a circular path is undergoing continuous acceleration, and an accelerating charged particle must continuously radiate energy. If the electron in Rutherford's model kept losing energy this way, it would spiral inward and eventually fall into the nucleus, which does not happen in reality — atoms are stable.
2. It could not explain the line (discrete) spectrum of atoms. Rutherford's model does not say anything about how electrons are distributed around the nucleus or what energies they have, and offers no explanation for why atoms emit or absorb light only at specific, discrete wavelengths (producing line spectra) rather than a continuous spectrum.

(A third valid drawback: it says nothing about the arrangement/distribution of electrons around the nucleus, i.e., how many electrons occupy which region.)

(iii) Photoelectric effect

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