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2-7: Summary of Part 2

Let us summarize what we have learned in Part 2.
(1) Through the discoveries of the radioactivity and the decay of radioactive elements, it has been realized that an atom has an internal structure and is not eternally constant but changeable.
(2) An atom has a structure in which a massive nucleus at the center is surrounded by light electrons.
(3) The size of the atomic nucleus is very small; its radius is less than
(4) The atomic nucleus has also an internal structure and is a changeable object. The proton is one of the constituents of the nucleus.

[The Difficulty in the Rutherford Model]
In the solar system, the planets are revolving around the sun. In the Rutherford model, the electrons are considered to move around the nucleus.
The attractive force between the sun and a planet is the universal gravitation. On the other hand, the force through which the nucleus attracts electrons is the Coulomb force. One might naively suppose that this Coulomb attractive force and the centrifugal force due to the orbital motion of the electron are just in balance to keep the system stable. However, this idea has a serious difficulty.
Now, let us explain this difficulty taking the case of hydrogen atom in which an electron (of mass m and charge e ) is moving around a proton. Suppose that, since the proton mass is large compared with that of electron, the proton stays at rest at the origin of the coordinate frame.
(A) The balance between the centrifugal force and the Coulomb force is written

The quantity on the left-hand side is the strength of the centrifugal force and the right-hand side the Coulomb force. Here r is the radius of the orbit of the electron, i.e. the radius of the hydrogen atom, and v is the speed of the electron. The above equation is rewritten

Looking at this equation only, we can think that the radius of the hydrogen is inversely proportional to the square of the speed of the electron, so that the hydrogen atom can have an arbitrary radius depending on the speed v. However, the realistic hydrogen is not so; the radius of the realistic hydrogen atom looks constant always.
(B) According to the theory of electromagnetism, any accelerating charged particle radiates electromagnetic waves, with losing the energy. Thus the electron in the Rutherford model must lose the energy to become out of balance and spiral inward, and finally collapse on the proton. This means that the hydrogen atom in the Rutherford model must be unstable. In contrast to this, however, a realistic hydrogen atom is quite stable and does not collapse.
Rutherford was well aware of this difficulty, but he chose to ignore it temporarily. Without solving this stability problem, we cannot look at the true feature of the microscopic world.
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