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?

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