Recall the two models

• Thomson model: atom is a uniformly positively charged sphere with electrons embedded in it.
• Rutherford model: almost all positive charge and mass are concentrated in a tiny nucleus; electrons revolve around it.

Check Option A

Option A says:

In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.

• In Rutherford's model, electrons revolve around the nucleus under electrostatic attraction. They are not in stable equilibrium; they have centripetal acceleration.
• In Thomson's model, if an electron is displaced inside a uniformly positively charged sphere, it can experience a restoring force; at the center net force can be zero.

So this statement is false.

Check Option B

Option B says:

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.

This is the reverse of the truth:

• In Thomson's model, positive charge (and hence mass, in that picture) is spread out more continuously.
• In Rutherford's model, mass distribution is highly non-uniform, concentrated in the nucleus.

So this statement is false.

Check Option C

Option C says:

A classical atom based on Rutherford's model is doomed to collapse.

In classical electrodynamics, a revolving electron is an accelerated charge, so it must radiate energy continuously. Hence its orbit would shrink and the electron would spiral into the nucleus.

Therefore, a classical Rutherford atom is indeed unstable and is doomed to collapse.

So Option C is true.

Check Option D

Option D says:

The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.

• In Rutherford's model, yes: the nucleus (positive part) contains nearly all the mass.
• In Thomson's model, the positive charge is spread throughout the atom and was not viewed as a tiny localized heavy nucleus. The statement as a comparison is not the standard distinguishing feature, and for a single-correct MCQ the clearly correct classical conclusion is Option C.

Hence D is not the intended correct option.

Final conclusion

The correct option is: $\boxed{\text{C}}$

Comparison with stored answer

Stored correct answer: C

My derived answer matches the stored answer.