Problem 7.45 Part A A radioactive nucleus at rest decays into a second nucleus,

Question

Problem 7.45 Part A A radioactive nucleus at rest decays into a second nucleus, an Determine the magnitude of the momentum of the second (recoiling) nucleus. electron, and a neutrino. The electron and neutrino are emitted at ight angles and have momenta of pe -9.70x10 2 kg.m/s and Py 5.83x10 23 kg.m/s, respectively. (Fiqure 1) Express your answer to three significant figures and include the appropriate units. ) ? PaucV Value Units Submit My Answers Give Up Part B Determine the angle between the momentum of the electron and the momentum of the second (recoiling) nucleus. Express your answer using three significant figures Submit My Answers Give Up Figure 1 of 1 +y +x 0

Explanation / Answer

Conservation of momentum requires that the momentum beofre the decay in the x direction b be equal to the momentum in the x direction after the decay. And same holds true for the y-direction.

So,

Pxi = Pxf = Pelectron + Pnucleusx

Pyi = Pyf = Pneutrino + Pnucleusy

But the initial nucleus is at rest so Pxi = Pyi = 0

Then Pelectron = - Pnucleusx = -9.7*10^-23 kg-m/s

Pneutrino = - Pnucleusy = -5.83*10^-23 kg-m/s

The magnitude |Pnucleus| = sqrt(Pnucleusx^2 + Pnucleusy^2)

|Pnucleus| = 1.13*10^-22 kg-m/s

Direction is q = 180 + arctan(Pnucleusy/Pnucleusx) = 211 degress

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