# Bohr's Model

In order to explain the stability of atoms and the discrete spectra emitted by atoms, Niels Bohr, in 1913, postulated the following two assumptions:- The electron in an atom can revolve around the nucleus only in certain allowed circular orbits without losing any energy.
- The electron can jump from one of the allowed orbits to another and can thereby gain or lose energy equivalent to the difference in energy of the two involved orbits.

where Îµ

_{0}is the permitivity of a vacuum (8.854 Ã— 10

^{-12}C

^{2}N

^{-1}m

^{-2}), r is the distance of the orbit from the nucleus and ï is the velocity of the electron in the orbit. According to Bohr, imposing the quantum mechanical restriction of angular momentum on the above expression can generate the allowed stationary orbit. The proposed restriction is that the angular momentum of the revolving electron is an integral multiple of the basic unit of h/2Ï€ , i.e.

Where n has integral values 1, 2, 3..., and is known as quantum number.

By combining the above equations one can obtain the following expressions for the stationary orbits:

From the above expressions, it follows that only certain orbits with precise energies are followed since the quantum number has only integral values 1, 2, 3... Now, the energy difference between any two energy states will be

Î”E = E

Î”E = E

_{2}- E_{1}The frequency of radiation carrying this energy difference will be given as and the wave number of radiation will be given as

where R is written for 2Ï€ ^{2}m (ï ^{2}/4Ï€ Îµ _{0})^{2}/h^{3}c and is known as the Rydberg constant. On substituting the values of m, e, Îµ _{0}, h and c, we find that

R = 1.09737 Ã— 10^{7} m^{-1}

The experimental value is found to be 1.09678 Ã—10^{7} m^{-1}.

The various Bohr orbits are schematical and the corresponding energy. The various electronic transitions of hydrogen atom. These transitions, which were also verified experimentally, are described in the table below: Five spectral series of hydrogen

**Limitations of Bohr's Theory**

Bohr's theory could explain all the experimental facts of the hydrogen atom but failed badly when applied to other atoms. Nevertheless, Bohr's theory has its own importance, as it was the first theory to introduce the concept of quantization in the behaviour of subatomic particles. Bohr's theory was abandoned 12 years after its formulation in favour of the present quantum theory of atomic structures.

**Drawbacks of Bohr's model**

- It fails to explain the spectra of multi-electron atoms (atoms having more than one electron).
- According to Bohr, the circular orbits of the electrons are planar. However, this is not true as the electrons move around the nucleus in three-dimensional space.
- It fails to explain the cause of chemical combination and shapes of the molecules arising out of it.
- One of the major drawbacks of Bohr's theory is that it assumes a definite knowledge about the position and momentum of electrons at the time of measurement. However, Heisenberg (1927) suggested that it is impossible to measure simultaneously both the exact position and momentum of a subatomic particle such as an electron. This statement is known as Heisenberg's uncertainty principle.
- It cannot explain the relative intensities of spectral lines.
- Bohr's theory failed to account for the splitting of spectral lines on the application of magnetic field (Zeeman effect) and also the application of the electric field (stark effect)