Question

47. A pion at rest (m_p = 273m_e) decays to a muon (m_m = 207m_e) and an antineutrino (m~0). Using SI units, find (a) the kinetic energy of the muon and (b) the energy of the antineutrino in joules.

Answer 1

Conserve energy and momentum using E = mc^2
Distribute this energy among the products by conserving linear momentum.

To calculate linear momentum of "antineutrino (m~0)" use
-de-Broglie equation
-E=hf

Answer 2

Unfortunately, de Broglie is from quantum mechanics which is the next chapter.

Answer 3

It's just an equation; you can use it anyway.. :)

Answer 4

LOL the only reason I know it is because I looked into the chapter. I have no clue how to apply it.

Answer 5

The equations are of the form -
E * λ = C1
λ * momentum = C2

where C1 and C2 are constants.

You just need to find momentum in terms of energy..

Answer 6

E^2 = p^2* c^2 + (mc^2)^2

Answer 7

@LastDayWork that's where the equation came from

Answer 8

Are you using this approach to calculate momentum of muon or antineutrino ??

Answer 9

no. but I need two equations for two unknowns; I'm currently in the process of trying to figure it out. Would you like me to send you the result I end up with?

Answer 10

Yea..coz I can't figure out what you just said..

Answer 11

@LastDayWork

Okay, you already know that this problem requires conservation of momentum and conservation of energy
1) P_a = P_m
2) E_pi = E_a + E_m

now, based on equation 39.27
The antineutrino is massless so with the second term gone, E_a = p_a*c
The muon however is not massless so E_m^2=(p_m*c)^2 + (m_m*c^2)^2

First solve for the energy of one particle and use the momentum relationship and the antineurtrino's energy as substitutions.

Because the antineutrino is massless, it's energy is simply it's momentum times the speed of light which can be found indirectly.

If you want a more specific response I can send it to you but typing it is going to be hell. Let me know.

Answer 12

Well, the above will do; I just wanted to see your approach.

I don't really know how the equation was derived (I know p is momentum; but is m rest mass or relativistic mass or mass defect). So, I can't help you here.

You should use relativistic mass for muon only if it is considerably close to speed of light (or else you'll unnecessarily complicate your calculations; and finally round off)