Compute the oscillation frequency (f) of the electron and the expected absorptio

Question

Compute the oscillation frequency (f) of the electron and the expected absorption or emission wavelength () in a Thomson-model hydrogen atom. Use R = 0.053 nm. Compare with the observed wavelength (observed) of the strongest emission and absorption line in hydrogen, 122 nm.

Here is an image: http://puu.sh/c113C/dab83545b7.png

I posted this also on a physics forum, but they take too long to respond, but this is what I posted there (my attempt at a solution): http://puu.sh/c118M/45d64fd679.png

Thanks

Explanation / Answer

In the Thompson model Centrifugal force= Electric Force:

Fcf = eE that is m*w^2*R =K*e^2/R^2     where K =9*10^9   (For hydrogen)

w^2 =K*e^2/(m*R^3) =9*10^9*(1.6*10^-19)^2 /9.1*10^-31/(0.53*10^-10)^3 =1.7*10^33 (rad/sec)^2

w =4.1239*10^16 rad/sec

The frequency of oscillation on this orbit is

F = w/(2*pi) =6.563*10^15 Hz

and the wavelength emitted in this circular motion is (since EM wave is emitted the speed is C)

lambda = C*T =C/F =3*10^8/6.56*10^15 =4.5708*10^-8 m =45.708 nm

lambda(observed)/lambda = 122/45.708 =2.669

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