A radioactive nucleus at rest decays into a second nucleus, an electron, and a n
ID: 1461022 • Letter: A
Question
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 9.40 10-23 kg·m/s, and 5.60 10-23 kg·m/s, respectively. What is the magnitude and direction of the momentum of the second (recoiling) nucleus?(Hint: Since momentum is a vector, use conservation of momentum in the two directions, independently.) What is the (a) Maginitude and (b) Direction measured from the direction opposite to the electron's momentum
Explanation / Answer
Since the original momentum was zero,the final momentum must be zero.therefore,the momentum of the second nucleus must equal the opposite of the sum of the momenta of the electron and the neutrino.
a) if we choose coordinates so that:
-electron momentum = x^9.40 e-23
-neutrino momentum = y^5.60 e-23
the second nucleus has momentum:
p= -e-23(x^9.4+y^5.6)
since sqrt(9.4^2+5.6^2)=10.94,
therefore magnitude of p= 10.94e-23 kg*m/.
b) Since both x^ and y^ components of momentum are negative,the direction is in quadrant 3 from the x^ axis : the tangent of the angel is 5.6/9.4=0.595, the angel from the x^ axis must be: 180 degrees +Arctan(0.595)= 180+30.75= 210.75 degrees