# Momentum Formula for Alpha Decay

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:

[itex]^{226}_{88}Ra[/itex] → [itex]^{222}_{86}Rn[/itex] + [itex]^{4}_{2}α[/itex] + [itex]Q[/itex]

and I want to find the kinetic energy of both the daughter Nucleus [itex]^{222}_{86}Rn[/itex], and also of the [itex]^{4}_{2}α[/itex] 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)

[itex]p=\frac{1}{2M_{Ra}}\sqrt{(M_{Ra}-(M_{Rn}-m_{α})^2)(M_{Ra}-(M_{Rn}+m_{α})^2)}[/itex]

and I have two equations for Kinetic Energies:

[itex]Ek_{α}=\sqrt{p^2+m_{α}^2}-m_{α}[/itex]

[itex]Ek_{Rn}=\sqrt{p^2+M_{Rn}^2}-M_{Rn}[/itex]

*My results:*

[itex]Ek_{α}≈4.8MeV[/itex]

[itex]Ek_{Rn}≈0.09MeV[/itex]

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

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