# Momentum Formula for Alpha Decay

[Mentor’s note: this thread does not use the standard homework-help template, because it was started in one of the non-homework forums. It was moved here because it had already gotten some help.]

Hi everyone. This isn’t a homework question, as I am just revising notes for my exams, and after extensive searching both online through search engines, and through browsing this forum, I did not seem to find any resource that can answer my question, so I just hope that somebody here can help me.

So let’s say we have an α-decay where:

$^{226}_{88}Ra$ → $^{222}_{86}Rn$ + $^{4}_{2}α$ + $Q$

and I want to find the kinetic energy of both the daughter Nucleus $^{222}_{86}Rn$, and also of the $^{4}_{2}α$ particle.

What information I have:

Equation for momentum p (I am not even sure if THIS is correct, the lecture notes that we have at our University are extremely confusing, and often omits working details and derivations)

$p=\frac{1}{2M_{Ra}}\sqrt{(M_{Ra}-(M_{Rn}-m_{α})^2)(M_{Ra}-(M_{Rn}+m_{α})^2)}$

and I have two equations for Kinetic Energies:

$Ek_{α}=\sqrt{p^2+m_{α}^2}-m_{α}$

$Ek_{Rn}=\sqrt{p^2+M_{Rn}^2}-M_{Rn}$

My results:

$Ek_{α}≈4.8MeV$
$Ek_{Rn}≈0.09MeV$

Could someone verify or explain me how the momentum p is Actually calculated for these particles? and then how to actually obtain those results (which are supposedly correct) for the Kinetic Energies?

http://ift.tt/1j3rn6w