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Hydrogen Spectrum Theory

Rutherford’s experiments on the scattering of -particles led Bohr to the conclusion that the atom consists of a positively charged nucleus at its centre. Moreover, Bohr applied the quantum theory of radiation as developed by Planck and Einstein to the Rutherford’s model. His theory is mainly based on the following postulates:

1. An atom consists of a positively charged nucleus at the centre.

2. The negatively charged particles known as electrons move round the nucleus in various orbits known as stationary energy levels. The electrons cannot emit radiations when moving in their own stationary levels.

3. The Coulombian and Newtonian forces are applicable in the domain of the atom.

4. The electrons revolve round the nucleus in various circular orbits and the angular momentum mvr = nh/2π where (n = 1, 2, 3, 4, etc) is called the quantum number, and h is the Planck’s constant.

5. When an electron jumps from a higher energy level to a lower energy level, it gives out electromagnetic radiation of a particular frequency.

W_n2 – W_n1 = hv

Where W_n2 is the energy of the n₂ energy level. W_n1 is the energy of the n₁energy level, and v is the frequency of the radiation.

Bohr’s postulates are the combination of some of the ideas of classical physics and quantum physics. While in some ways they agree with classical physics but in some aspects they are contradictory to it. Here the energy levels are quantized. It means that the electrons can move only in some particular orbits of definite radii and not at all radii as suggested by Rutherford’s model.

Consider an atom whose nucleus has n positive charge E and let an electron of negative charge e move round the nucleus in an orbit of radius r.

E = Ze, where Z = 1 for hydrogen.

The force of attraction between the nucleus and the electron

As the electrons move along the circular orbit, the centripetal forceis provided by the attractive force on the electron.

The angular momentum, mvr = nh/2π          (iii)

Substituting the value of v in equation (ii),

Substituting this value of r in equation (v)