4. BOHR’S MODEL FOR HYDROGEN ATOM

BOHR’S MODEL OF ATOM

Niels Bohr in 1913, proposed a new model of atom on the basis of Planck’s Quantum Theory. The main points of this model are as follows:
(i) In an atom, the electrons revolve around the nucleus in certain definite circular paths called orbits.
(ii) Each orbit is associated with definite energy and therefore these are known as energy
levels or energy shells. These are numbered as 1, 2, 3, 4……….. or K, L, M, N………..
(iii) Only those energy orbits are permitted for the electron in which angular momentum of the electron is a whole number multiple of h/2π
Angular momentum of electron (mvr) = nh/2π (n = 1, 2, 3, 4 etc).
m = mass of the electron.
v = tangential velocity of the revolving electron.
r = radius of the orbit.
h = Planck’s constant.
n is an integer.
(iv) As long as electron is present in a particular orbit, it neither absorbs nor loses energy and its energy, therefore, remains constant.
(v) When energy is supplied to an electron, it absorbs energy only in fixed amounts as quanta and jumps to higher energy state away from the nucleus known as excited state. The excited state is unstable, the electron may jump back to the lower energy state and in doing so, it emits the same amount of energy. (∆E = E₂ – E₁).

• Achievements of Bohr’s Theory
1. Bohr’s theory has explained the stability of an atom.
2. Bohr’s theory has helped in calculating the energy of electron in hydrogen atom and one electron species. The mathematical expression for the energy in the nth orbit is,
The main achievements of Bohr’s theory of the atom are:
1.    It can explain the stability of atom.
2.    It successfully explain the line spectrum of hydrogen.
3.    It explain the line spectra of single electron ions like He⁺ and Li²⁺

• Limitations of Bohr’s Model
(i) The theory could not explain the atomic spectra of the atoms containing more than one electron or multi electron atoms.
(ii) Bohr7s theory failed to explain the fine structure of the spectral lines.
(iii) Bohr’s theory could not offer any satisfactory explanation of Zeeman effect and Stark effect.
(iv)Bohr’s theory failed to explain the ability of atoms to form molecule formed by chemical bonds.
(v) It was not in accordance with the Heisenberg’s uncertainty principle.