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In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
An atom has a nearly continuous mass distribution in a Rutherford's model but has a highly non-uniform mass distribution in Thomson's model
A classical atom based on Rutherford's model is doomed to collapse.
The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.
Solution
According to Rutherford, $e ^{-}$revolves around nucleus in circular orbit. Thus $e ^{-}$is always accelerating (centripetal acceleration). An accelerating change emits $EM$ radiation and thus $e ^{-}$ should loose energy and finally should collapse in the nucleus.