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 nucleus was at rest at the origin of an coordinate system. The electron moves away from the origin with linear momentum 1.35 x 10-22 kg m/s directed along the x-axis ; the neutrino moves away from the origin with linear momentum 6.1 x 10-23 kg m/s directed along the y-axis.  
(a) What is the magnitude of the linear momentum of the daughter nucleus ? Answer in units of 10-22 kg m/s--no unit is necessary in the text box.

(b) If the mass of the daughter nucleus is 6.2 x 10-26 kg, what is it's final velocity?

Explanation / Answer

a)

as per conservation of momentum

initial total momentum = final total momentum

0 = momentum of electron + momentum of nutrino + momentum of nucleus

0 = (1.35 x 10-22) i + (6.1 x 10-23) j + Pnucleus

Pnucleus = - (1.35 x 10-22) i - (6.1 x 10-23) j

magnitude = sqrt((1.35 x 10-22)2 + (6.1 x 10-23)2) = 1.48 x 10-22 kgm/s

b)

mn = mass of nucleus = 6.2 x 10-26 kg

V = final velocity

Pnucleus =mn V

- (1.35 x 10-22) i - (6.1 x 10-23) j = (6.2 x 10-26) V

V = - ((1.35 x 10-22)/ (6.2 x 10-26)) i - ((6.1 x 10-23)/ (6.2 x 10-26)) j

V = - 2177.42 i - 983.87 j

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