Bohr Atomic Model

Bohr adopted Rutherford model of the atom & added some arbitrary conditions. These conditions are known as his postulates:

(i) The electron in a stable orbit does not radiate energy, i.e.,

(ii) A stable orbit is that in which the angular momentum of the electron about nucleus is an integral (n) multiple of

i.e. m ;

where n = 1, 2, 3,………….()

(iii) The electron can absorb or radiate energy only if the electron jumps from a lower to a higher orbit or falls from a higher to a lower orbit.

(iv) The energy emitted or absorbed is a light photon of frequency and of energy

E = h

For hydrogen atom : (Z = atomic number = 1)

(i) = angular momentum in the nth orbit = .

(ii) = radius of nth circular orbit = (0.529 A°); (1A° = m).

(iii) = Energy of the electron in the nth orbit = eV

Binding Energy = -eV

(iv) = Energy emitted when an electron jumps from n₂ orbit to n₁ orbit (>).

(v) For hydrogen like atom/species of atomic number Z:

Bohr's explanation of Spectral of Hydrogen Atom

(i) Lyman Series:

Bohr postulated that Lyman series of obtained when an electron jumps to the first orbit (n₁ = 1) from any outer orbit (n₂ = 2, 3, 4 ........)

where n₂: 2, 3, 4............ This series lies in the ultra violet region of the spectrum and agree well with the values of s observed experimentally by Lyman.

(ii) Balmer Series:

According to Bohr, Balmer series is obtained when an electron jumps to the second orbit (n₁ = 2) from any outer orbit (n₂ = 3, 4, 5 .......) Wave number of these spectral lines is

where n₂ = 3, 4, 5......... This series lie in the visible part of the spectrum.

(iii) Paschan Series:

According to Bohr Paschen series is obtained when an electron jumps to the 3_rd orbit (n₁ = 3) from any out of orbit (n₂ = 4, 5, 6......) Bohr calculated the wave number of spectral lines of Paschen series from the relation.

where n₂ = 4, 5, 6 ........ This series lies in the infrared region of the spectrum.

(iv) Paschan Series:

According to Bohr, Brackett series is obtained when an electron jumps to the 4th orbit (n₁= 4) from any out orbit (n₂ = 5, 6, 7 ..........). This series lie in far infrared region.

where n₂ = 5, 6, 7……….

(v) Pfund Series:

According to Bohr, Pfund series is obtained when an electron jumps to the 5th orbit (n₁ = 5) from any outer orbit (n₂ = 6, 7, 8........). This series lies in far infrared region.

where n₂ = 6, 7, 8 .............

Energy Level Diagram:

A diagram which represents the total energies of electron in different stationary orbits of an atom are called the energy level diagram and are represented by parallel horizontal lines. Total energy in the nth orbit of hydrogen atom is given by

E =

On substituting the values, we get

E = eV

Substituting n = 1, 2, 3,............, we get the energies of electrons in various stationary orbits as:

E₁ = = -13.6eV

E₂ = = -3.4eV

E₃ = = -1.51.6eV

E₄ = = -0.85eV

E₅ = = -0.54eV

E₆ = = -0.37eV

E₇ = = -0.28eV

Clearly, as n increases, E_n becomes less negative until at n = ∝, E_n = 0

Limitations of Bohr's Theory:

Ø This theory is applicable only to simplest atom like hydrogen, with Z = 1. The theory fails in case atoms of other elements for which Z > 1

Ø The theory does not explain why orbits of electrons are taken as circular, while elliptical orbits are also possible.

Ø Bohr's theory does not explain the fine structure of spectral lines even in hydrogen atom.

Ø Bohr's theory does not say anything about the relative intensities of spectral lines.

Ø Bohr's theory does not take into account the wave properties of electrons.