Rutherford's nucleus model

According to this model most of the mass of atom and all its positive charge are concentrated in tiny nucleus, and electrons in the atom revolve around it. This model of atomic structure emerged from Geiger - Marsden experiment in 1911 in which a collimated beam of 5.5 MeV alpha particles from bismuth was allowed to fall on 2.1 x 10-7 mm thin gold foil. The scattered alpha particles produced scintillations on ZnS screen, which were counted at different angles (θ) from the direction of the beam.. though most of the alphs particles suffer negligible deviation , some (about one in 104) suffered a large change in direction (θ>90) The last observation gave crutial clue to the nuclear model.
            Rutherford's calculation used the inverse square law of repulsive force between alpha particle and the gold nucleus. Multiple scattering was ignored. The scattering angle θ of alpha particle is related to impact parameter b by the relation
b=[Ze2 cot(θ/2)]/[4πε0(mv2/2)]
where impact parameter is defined as the perpandicular distance of the initial velocity vector of the alpha particle from the centre of the nucleus.  The observed number of scattered alpha particles at different angles agreed with Rutherford's calculation based on the nuclear model of atom.
               Classically Rutherford's model of atom is unstable because an orbiting electron accelerates continously and must loose its energy as EM radiation. The orbit should shrink spiraly into the nucleus within 10-8 sec and gives out continous spectrum of radiation. But we now that hydrogen atom is stable and has a characterstic line spectrum . This difficulty of unstable and shrinking orbits was taken care in Bohr's model of hydrogen atom and would be discussed later.

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