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A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The...

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 9.10×10−23 kg⋅m/s and , 6.25×10−23 kg⋅m/s respectively.

a) Determine the magnitude of the momentum of the second (recoiling) nucleus.

b) Determine the direction of the momentum of the second (recoiling) nucleus. Assume that the neutrino and the electron move along −x and −y axes respectively.

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Homework Answers

Answer #1

a)

Given

Pneutrino =(-6.25*10-23) i (since it is moving along -x-axis)

PElectron=(-9.1*10-23) j (since it is moving along -y axis)

By Conservation of momentum

Pinitial = PFinal

Initial radioactive nucleus at rest PInitial =0

0 =Psecond Pelectron + Pneutrino

0 = Psecond + (-6.25*10-23i ) +(-9.1*10-23j)

Psecond = (6.25*10-23)i +(9.110-23)j

The magnitude of the momentum of the second recoiling nucleus

|Psecond| = sqrt[(6.25*10-23)2+(9.1*10-23)2] = 1.104*10-22 kg-m/s

b)

Direction

o = tan-1(9.1*10-23/6.25*10-23) = 55.52o

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