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Dalton’s atomic theory

Thomson’s atomic model

Limitations of Thomson’s atomic model

Rutherford’s atomic model

Scattering of alpha particles

Electrostatic force between the nucleus and α–particle

Distance of closest approach

Impact parameter

Rutherford’s scattering formula

Limitations of Rutherford atomic model

Bohr’s atomic model

Radius of orbit of electron

Velocity of electron in an orbit

Frequency of electron

Time period of revolution of an electron

Kinetic energy of an electron revolving in an orbit

Potential energy of an electron in an orbit

Total energy of an electron in an orbit

Wave number of an electron in an orbit

Quantum numbers

Hydrogen spectrum series

Lyman series

Balmer series

Paschen series

Brackett series

Pfund series

Line spectra and electron transitions between energy levels

de Broglie’s explanation of Bohr’s second postulate of quantisation

Limitations of Bohr’s atomic model



Rutherford’s atomic model


Scattering of alpha particles


Graph of scattering angle and number of partcles


On the basis of α–particle scattering experiment, Rutherford made following observations.

The entire positive charge and almost entire mass of the atom is concentrated at its centre in a very tiny region of the order of 10-15 m, called nucleus.

He proposed the following model for the structure of atom.

  1. The negatively charged electrons revolve around the nucleus in different orbits.

  2. The total positive charge on the nucleus is equal to the total negative charge on electron. Therefore atom as a whole is neutral.

  3. The electrons revolve around the nucleus. The centripetal force required by electron for revolution is provided by the electrostatic force of attraction between the electrons and the nucleus.

Electrostatic force between the nucleus and α–particle

When the α–particle approaches a nucleus with atomic number Z (+ve charge Ze) the magicnitude of this electrostatic force


Distance of closest approach

ro  = 14πεo 2Ze2EK

where, EK = kinetic energy of the α-particle.

Impact parameter

The impact parameter is the perpendicular distance of the initial velocity vector of the α-particle from the centre of the nucleus.

b=14πεo Ze2cot θ2EK 

Rutherford’s scattering formula

N(θ)= Nint Z2e48πεo2 r2E2 sin4θ2


N(θ) = number of α–particles with scattering angle θ,

Ni = total number of α-particles reaching the screen,

n = number of atoms per unit volume in the foil,

Z = atomic number of the foil,

E = kinetic energy of the alpha particles and

t = foil thickness

Limitations of Rutherford’s atomic model

  1. About the stability of atom - According to Maxwell’s electromagnetic wave theory electron should emit energy in the form of electromagnetic wave during its orbital motion. Therefore radius of orbit of electron will decrease gradually and ultimately it will fall in the nucleus.


  1. About the line spectrum - Rutherford atomic model cannot explain atomic line spectrum.