Pakistan study notes for Matric, Intermediate, B.A, B.COM BSC, M.A, BCS. Free Pakistani Urdu educational school, colleges and University notes.



In order to improve the Rutherford’s model and to explain the line spectra of elements, Niels Bohr (1885-1962) a Danish physicist working in Rutherford’s laboratory proposed a theory for the electron structure of atom in 1913.


Bohr assumed that on the basis of the quantum theory, there exists the possibility that electron in certain orbits may not give out radiation and an electron revolving in any one of such orbits would be completely stable, Such orbits were called ‘Stationary states’. Bohr envisioned the stationary states as circular orbits around the nucleus. He considered that an electron in a certain orbit has certain energy and as long as it keeps revolving in that orbit, it neither absorbs nor radiates energy. If the electron absorbs energy equal to the energy difference between the two orbits, the electron is excited, i.e. it jumps to higher energy state. If it falls back to lower level, it must emit energy equal to the energy difference between the two orbits. (Fig: 3.11). lf this energy is absorbed or emitted as light, a single photon (quantum) of absorbed or emitted light must account for the required energy differences, so that on the basis of h

hu = ΔE

Where ΔE is the difference between the energies of the final and initial orbits, h= Planck’s constant (6.625 x 10-34 J.S.) which has the dimensions of energy X time.


Bohr assumed that all the transitions that electrons make between two orbits, yield a single unique spectral line.

Bohr further assumed that the stationary states were only those orbits in which the product momentum (mv) x circumference (2 π r), sometimes called the action’, was equal to the Planck’s constant ‘h’ or some integral multiple of ‘h’ therefore for the first possible orbit.

momentum circumference = h

mv x 2 π r = h

or for any other orbit,

mv x 2 π r = nh


Where ‘n’ was a simple integer, n = l for first orbit, n = 2 for the second and so on.

This equation could be re-written as,

mvr = nh/ 2π

Here ‘mvr’ becomes the angular momentum of the electron, Thus Bohr’s first condition defining the stationary states could be stated as,


“Only those orbits were possible in which the angular momentum of the electrons would be an integral multiple of h /2π. These stationary states correspond to energy levels in the atom”.

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