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TheAustrian
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[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?
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?
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