Why is the sky blue?
Where x is the displacement from the centre of the electron cloud to the nucleus, q is the charge of the nucleus and q’ is the reduced charge contained in the spherical portion of the electron cloud of radius equal to the displacement of the nucleus. The outer shell does not exert a force on the nucleus by Newton’s shell theorem.We have assumed charge to be evenly distri cloud so q’ is proportional to the volume of the reduced electron cloud. Let V be the volume of the buted in the electron
reduced electron cloud and be the constant charge density of the electron cloud:
Substituting this into (2),
.
The Coulomb force is proportional to the displacement of the nucleus from its equilibrium position, obeying Hooke’s Law. Hence it can also be written as
where m is the mass of the body on the spring and F(x) is the attraction exerted by the electron cloud on the nucleus, and by Newton’s third law reciprocated by the electron cloud but in the opposite direction:
is the natural angular frequency of the system. F(x) is
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