An early model of the hydrogen atom considered the atom to consist of a proton, which is a uniform charged sphere of radius R, with an electron in an orbit of radius r0 inside the proton as shown in Figure.

(a) Use Gauss's law to obtain the magnitude of E (the field due to the proton) at the position of the electron. Give your answer in terms of e (the charge on a proton), r0, and R.

(b) Find the frequency of revolution f in terms of r0 and the velocity of the electron v.

(c) What is the force on the electron in terms of m,v, and r0?

(d) What is the frequency f in terms of m, e, R, e0 , and r0?

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Electron Proton