A radioactive nucleus at rest decays into a second nucleus, an electron, and a n

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 9.00 10-23 kg·m/s, and 5.20 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.)

Magnitude
_________kg·m/s
Direction
__________° (measured from the direction opposite to the electron's momentum

Explanation / Answer

first the magnitude of the momentum is

P = sqrt(( 9 * 10^-23)^2 + ( 5.2 * 10^-23)^2)

P = 1.04 * 10^-22 kg m/s

then the direciton is

theta = 180 - tan^-1((5.2 * 10^-23) / ( 9 * 10^-23)) = 180deg - 30.02deg = 149.98 deg

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