A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton (mass 1.67×10−²⁷ kg) and an electron (mass 9.11×10−³¹ kg) . The proton and electron were shot out back-to-back. The proton speed was measured to be 1.0 ×10⁵ m/s and the electron speed was 3.0×10⁷ m/s . No other decay products were detected. c. How much momentum did this neutrino 'carry away' with it?

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1. Identify the law of conservation of momentum which states that the total momentum of a closed system is constant if no external forces are acting on it. Since the neutron decays into a proton and an electron, the vector sum of the momenta of the proton and electron should equal the initial momentum of the neutron, which is zero as the neutron was initially at rest.
2. Calculate the momentum of the proton using the formula \( p = mv \), where \( m \) is the mass of the proton and \( v \) is its velocity. Substitute the given values for the mass and velocity of the proton.
3. Calculate the momentum of the electron using the same momentum formula \( p = mv \), substituting the given values for the mass and velocity of the electron.
4. Since the neutron was initially at rest, its initial momentum was zero. According to the conservation of momentum, the vector sum of the momenta of the proton and electron should also be zero. This means the momentum vectors of the proton and electron are equal in magnitude but opposite in direction.
5. If there is any discrepancy in the magnitudes of the calculated momenta of the proton and electron, this discrepancy would indicate the momentum carried away by the neutrino. Calculate the difference between the magnitudes of the proton's and electron's momenta to find the magnitude of the momentum carried away by the neutrino.