A certain radioactive (parent) nucleus transforms to a different (daughter) nucl

Question

A certain radioactive (parent) nucleus transforms to a different (daughter) nucleus by emitting an electron and a neutrino. The parent was at rest at the origin of an xy coordinate system. The electron moves away from the origin with linear momentum (-5.6 x 10-22 kg m/s) ; the neutrino moves away from the origin with linear momentum (-6.9 x 10-23 kg m/s) . What are (a) the magnitude and (b) angle (from the +x axis) of the linear momentum of the daughter nucleus? (c) If the daughter nucleus has a mass of 8.7 x 10-26 kg, what is its kinetic energy?

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Explanation / Answer

It appears the electron and neutrino both move in negative x direction. So teh daugher nuclersud must move in +ve x direction making zer0 angle and magnitude would be the sum of the magnitudes. Let Pbe teh magnitude of momentum of daughetr nucleus, then P = (9.6+0.13)*10^-22 kg m s^-1 = 9.73*10^-22 kg m s^-1. Its kinetic energy, KE is given by P^2 / (2m) KE = [9.73^2/(2*3.5)]*10^-18 J = 13.52*10^-18 J

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