How Quickly Does an Electron Spiral into the Nucleus in Classical Physics?

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Homework Statement

According to classical physics, a charge e moving with an acceleration a radiates at a rate
dE/dt = - (e²a²)/(6pi epsilon c³)

a) Show that an electron in a classical hydrogen atom spirals into the nucleus at a rate
dr/dt = - e⁴/ (12pi^2 epsilon^2 r^2 m_e^2c³)

b) Find the time interval over which the electron will reach r = 0, starting from r_o = 2.00 X 10^-10 m.

Homework Equations

None

The Attempt at a Solution

We are not sure how to relate energy with radius.

 

[jpreed]

From a purely classical standpoint you can ask:

-what is energy of a ground state electron in a hydrogen atom?

-what is the starting radius of the electron in a hydrogen atom?

-we assume, it is moving in a circle, so what is the formula for its kinetic energy?

You should be able to answer these questions and then use conservation of energy to put together a formula for the energy as a function of radius.

From there you can solve the problem.

Hope this helps!