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What is Bohr's model of the atom?

Class 11 ChemistryNCERT chapter: Structure of Atomइसे हिंदी में पढ़ें

Exam-ready answer

Bohr's model of the hydrogen atom states that the electron revolves around the nucleus in fixed circular paths called orbits or stationary states, each with a definite energy. While in an orbit, the electron does not lose energy. Its angular momentum is quantised, mvr = nh/2π. Energy is absorbed or emitted only when the electron jumps between orbits, with ν = ΔE/h.

Explanation

Rutherford's nuclear model could not explain why an orbiting electron does not radiate energy and spiral into the nucleus, or why hydrogen gives a line spectrum. Niels Bohr in 1913 used Planck's quantum idea to fix this. His first postulate: the electron in a hydrogen atom moves around the nucleus in circular paths of fixed radius and energy, called orbits, stationary states or allowed energy states, arranged concentrically.

Second, the energy of an electron in an orbit does not change with time. It moves to a higher orbit only by absorbing the right amount of energy and falls back by emitting it. Third, the frequency of radiation absorbed or emitted is ν = ΔE/h = (E₂ − E₁)/h, which is Bohr's frequency rule. Fourth, the angular momentum of the electron is quantised: mₑvr = nh/2π, where n = 1, 2, 3 and so on.

From these postulates, the radius of the nth orbit is rₙ = n²a₀, with a₀ = 52.9 pm, and the energy is Eₙ = −R_H(1/n²), where R_H = 2.18 × 10⁻¹⁸ J. The negative sign means the bound electron has lower energy than a free electron. The model explains the hydrogen line spectrum and hydrogen-like ions such as He⁺ and Li²⁺, but it fails for multi-electron atoms, the Zeeman and Stark effects, and ignores the dual nature of the electron and the uncertainty principle.

Points to remember

  1. Stationary states: fixed circular orbits of definite energy in which the electron does not radiate energy.
  2. Quantisation of angular momentum: mₑvr = nh/2π (n = 1, 2, 3…).
  3. Bohr's frequency rule: ν = ΔE/h = (E₂ − E₁)/h for absorption or emission between orbits.
  4. For hydrogen: rₙ = n² × 52.9 pm and Eₙ = −2.18 × 10⁻¹⁸ (1/n²) J; for hydrogen-like ions Eₙ = −2.18 × 10⁻¹⁸ (Z²/n²) J.
  5. Limitations: cannot explain spectra of multi-electron atoms, fine lines, Zeeman and Stark effects; ignores dual nature and the uncertainty principle.

Exam tip

Write the postulates as numbered points, then the two formulas mₑvr = nh/2π and ν = ΔE/h. If the question asks for five marks, add rₙ, Eₙ and two limitations; a simple diagram of concentric orbits with an electron jump earns extra clarity.

Questions students also ask

Why is the energy of an electron in Bohr's orbit negative?
The zero of energy is taken for an electron completely free from the nucleus (n = ∞). When the electron is attracted and bound to the nucleus, its energy becomes lower than this, so it is negative. The more tightly bound the electron (smaller n), the more negative its energy.
How does Bohr's model explain the line spectrum of hydrogen?
Each orbit has a fixed energy, so when the electron falls from a higher orbit to a lower one it emits a photon of a fixed energy ΔE and frequency ν = ΔE/h. Only certain jumps are possible, so only certain wavelengths appear, giving separate lines instead of a continuous spectrum.
What are the main limitations of Bohr's model?
It cannot explain the spectra of atoms with more than one electron, the fine doublet lines seen with better spectroscopes, or the splitting of lines in magnetic (Zeeman) and electric (Stark) fields. It treats the electron as a particle on a fixed path, ignoring its wave nature and Heisenberg's uncertainty principle.

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