A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. the electron and neutrino are emitted at right angles and have momenta of 9.80 ✕ 10-23 kg·m/s, and 5.70 ✕ 10-23 kg·m/s, respectively. what is the magnitude and direction of the momentum of the second (recoiling) nucleus?

Respuesta :

W0lf93
Since the electrons and neutrino are emitted at rigt angles, the nucleus is emitted at opposite side to right angle. So Pe , Pnue and Pnu are the momentum vectors. 
Then Pnu^2 = Pe^2 + Pnue^2 => (9.80 âś• 10-23)^2 + (5.70 âś• 10-23)^2 
Pnu^2 = 128.53 x 10^-46 
Pnu = 1.13 x 10^-22 kg-m/s 
The momentum is in quadrant 3 along positive x axis with angle of direction = 180 + arctan (Pnue/Pe) = 180 + 30 (approx) = 210 degrees