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Bohr Model of the Hydrogen Atom

Bohr's model of hydrogen states that the electron can revolve only in certain stable stationary orbits without radiating energy, and radiation is emitted or absorbed only when the electron jumps between allowed energy levels.

In one line: Bohr orbits are allowed parking levels; light appears only when the electron changes level.

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Understand it

  • Bohr modified the Rutherford model by adding quantum conditions.
  • The electron is allowed only in orbits where its angular momentum is an integral multiple of h divided by 2π.
  • While in such an orbit, it does not radiate energy.
  • When it moves from a higher energy level to a lower energy level, it emits a photon; when it absorbs the right energy, it moves to a higher level.
  • The model works best for hydrogen and hydrogen-like single-electron species.

Example

For hydrogen, the first orbit has n = 1 and the second orbit has n = 2. A transition from n = 3 to n = 2 gives a photon in the Balmer series because the final level is n = 2.

Formula and rule

Angular momentum quantisation: L = mvr = nh/2π, where m is electron mass in kg, v is orbital speed in m s−1, r is orbit radius in m, n is the principal quantum number, and h is Planck's constant in J s.

Transition rule: hν = Ei - Ef for emission, where ν is frequency in Hz and energies are in joule or consistently in eV.

Use for hydrogen or hydrogen-like one-electron systems.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

An electron in hydrogen jumps from n = 3 to n = 2.

  1. 1Using En = -13.6/n2 eV, E3 = -13.6/9 = -1.51 eV and E2 = -13.6/4 = -3.40 eV.
  2. 2Photon energy for emission = E3 - E2 = (-1.51) - (-3.40) = 1.89 eV.
  3. 3Interpretation: the atom emits a photon of energy 1.89 eV in the Balmer series.

Method you can reuse

  1. 1Write the relevant Bohr postulate.
  2. 2Identify n, initial level, and final level.
  3. 3Apply L = nh/2π for orbit questions or hν = energy difference for transition questions.
  4. 4Keep units consistent.
  5. 5Interpret whether the transition is emission or absorption.

Sketch it in your answer

Draw a central nucleus with circular allowed orbits labelled n = 1, n = 2, n = 3. Show an inward arrow for emission and an outward arrow for absorption. Label photon hν for the transition.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What are the two main quantum ideas in Bohr's model of hydrogen?

Think first, then show answer
Bohr's model says that only certain stationary orbits are allowed, with angular momentum L = nh/2π, and that light is emitted or absorbed only when the electron jumps between these allowed energy levels with photon energy equal to the energy difference.

Common wrong answer

A common wrong answer is taking the numerical energy difference as negative for emitted photon energy. Photon energy must be reported as a positive amount; the atom's energy decreases during emission.

Don't mix this up

Students often use hν = Ef - Ei for emission without checking signs. For emission from higher to lower level, photon energy is Ei - Ef, a positive value.

Exam tip

Always identify initial and final levels first. For emission, higher n to lower n; for absorption, lower n to higher n.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask for Bohr's postulates, the meaning of stationary orbit, angular momentum quantisation, photon energy in a transition, or why Bohr's model improves Rutherford's model.
  1. 1

    Enough for 1 mark

    Bohr's model of hydrogen states that the electron can revolve only in certain stable stationary orbits without radiating energy, and radiation is emitted or absorbed only when the electron jumps between allowed energy levels.

  2. 2

    Add for 2 marks

    Example: For hydrogen, the first orbit has n = 1 and the second orbit has n = 2. A transition from n = 3 to n = 2 gives a photon in the Balmer series because the final level is n = 2.

  3. 3

    Add for 3 marks

    Bohr modified the Rutherford model by adding quantum conditions.

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