Understanding Electron Motion in the Thomson Model of the Atom: Where to Begin?

[CollectiveRocker]

Can someone please give me a nudge in the right direction on how to solve this problem? The electric field intensity at a distance r from the center of a uniformly charged sphere of radius R and total charge Q is Qr/4πεR^3, when r < R. Such a sphere corresponds to the Thomson model of the atom. Show that an electron in this sphere executes simple harmonic motion about its center and derive a formula for the frequency of motion. Evaluate the frequency of the electron oscillations for the case of the hydrogen atom and compare it with the frequencies of the spectral lines of hydrogen. How do i even start?

 

[HallsofIvy]

You start with "F= ma". F, the force on an electron with charge e, is -Qer/(4πεR^3) so ma= m (d²r/dt²= -(Qe/(4πεR³)) Can you solve that differential equation? (Note that Qe/(4πεR^{3[/sup) is a constant.)}

 

[ZapperZ]

You start with "F= ma". F, the force on an electron with charge e, is -Qer/(4πεR^3) so ma= m (d²r/dt²= -(Qe/(4πεR³)) Can you solve that differential equation? (Note that Qe/(4πεR^{3[/sup) is a constant.)}

<sup>I think you may have missed a factor of "r" in your differential equation. This is the crucial piece that makes it have a sinusoidal solution.

Zz.</sup>