Exploring the Anatomy of Compton Scattering

[neilparker62]

Introduction
In this article we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article:
 

 
From the above equations, Compton solved for two variables namely $\beta$ the ratio of electron speed to the velocity of light, and for $\nu_{\theta}$, the frequency of the scattered photon. He re-wrote the solution for the second in wavelength form as it is commonly presented (albeit requiring us to replace $2\sin^2 \frac{\theta}{2}$ with $1-\cos\theta$ where $\theta$ is the scattering angle):

It is not quite clear why Compton wrote out the cosine rule with a “+” sign rather than a “-” in Equation 1 but, as noted by PF user...

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[fizzle]

We have the beginning electron speed (zero) and the final speed, is there an equation or graph of the electron's speed (or acceleration) between those two points in time?

Thanks

 

[neilparker62]

Not that I'm aware of. Most conservation of momentum problems and/or collision problems are dealt with using equations which do not consider transients. For example a bouncing ball experiences very rapid deceleration and acceleration in the opposite direction when it hits the floor. But you don't get many problems which focus on that part of the motion.