Difference between Rutherford model of hydrogen atom and Bohr Model of Hydrogen Atom

Rutherford model of hydrogen atom:

·        Rutherford thought that the atom is similar to the solar system this was the result of his experiment in which he bombards the atoms by alpha rays (He²⁺) and from the observations he put the following postulates:

a)     Atoms have a nucleus in the center with positive charge and there are large spaces in the atom.

b)    Electrons revolve around nucleus in such a way that attractive forces = centrifugal forces. These two forces equal in value and opposite in direction.

Instability of Rutherford model:

·        The following limitations found in Rutherford model of atoms:

     a)     According to classical thermodynamics a negative charge revolving around positive charges experiences continuous acceleration and should radiate continuous energy. Losing energy make electron come nearer from nucleus till it fall in it.

     b)    According to this model there will be continuous spectra instead of experimentally determined discrete spectra.

Bohr model of hydrogen atom:

·        Bohr postulates the following:

a)     The electron in an atom can revolve around the nucleus only in certain allowed circular orbits without losing energy i.e. E (energy of orbit) and r (radius of orbit) are constants.

b)    The electron can jump from one allowed orbital to another allowed orbital by gain or loss energy equivalent to the energy difference between the two orbitals.

c)     The angular momentum of electron is given by

Where, n is quantum no. takes integral values. And equal to the number of orbitals in atom

Limitation of Bohr Theory:

a)     Bohr theory failed completely when applied to atoms containing more than one electron.

b)    Bohr theory provides no explanation for the relative intensities of various spectral lines and splitting of these lines in presence of magnetic or electric fields

Energy of spectral lines of hydrogen atom:

 According to Bohr’s postulate, atom emit radiations only when the electron jumps from orbit of higher energy to orbit of lower energy

                                         ΔE = E_n2 - E_n1  

          Where,  n₂  orbit of higher energy (higher quantum no.)

                         n₁  orbit of lower energy (lower quantum no.)

 

In terms of wave number the energy difference is:

R_H  is Rydberg constant for hydrogen = 3.2902 x 10¹⁵ S^-1

In terms of wavelength:

                      

R_H  is Rydberg constant for hydrogen= 1.0972x10⁷ m^-1 = 1.0972x10⁵ cm^-1 = 109,700 cm^-1

 Five different series for atomic hydrogen can be observed each series consist of spectral lines that can be calculated from the previous equation as follow:

               Lyman series n₁ =1                 n₂ = 2, 3, 4….

               Balmer series n₁ =2                 n₂ = 3, 4, 5….

               Paschen series n₁ =3                 n₂ = 4, 5, 6….

               Brackett series n₁ =4                 n₂ = 5, 6, 7….