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 $(mass1.67\times {10}^{-27}kg)$and an electron $(mass9.11\times {10}^{-31}kg)$. The proton and electron were shot out back-to-back. The proton speed was measured to be $1.0\times {10}^{5}m/s$and the electron speed was $3.0\times {10}^{7}m/s$. No other decay products were detected.

a. Did momentum seem to be conserved in the decay of this neutron?

b. If a neutrino was emitted in the above neutron decay, in which direction did it travel? Explain your reasoning.

c. How much momentum did this neutrino “carry away” with it?

Step by step solution

01

Step 1. Given information is :mass of proton = 1.67×10-27kgmass of electron = 9.11×10-31kgSpeed of proton = 1.0×105m/sSpeed of electron = 3.0×107m/s

We need to find out :

a) Whether momentum is conserved or not.

b) Direction of neutrino emitted.

c) Momentum carried by neutrino.

02

Step 2. Applying Law of conservation of Momentum

As Per Law of conservation of momentum,
$$\begin{gathered} P_i=P_f \\ Weknowthat, \\ {P}_i=0 \\ and{P}_f=m_p{v}_p+m_e{v}_e \\ =(1.67\times {10}^{-27}kg)(1.0\times {10}^{5}m/s)+(9.1\times {10}^{-31}kg)(-3\times {10}^{7}m/s) \\ \left[Negativeasdirectionofelectronwillbeopposite\right] \\ =1.3967\times {10}^{-22}kgm/s\ne 0 \\ As{P}_i\ne P_f \\ Momentumisnotconserved. \end{gathered}$$

And if Neutrino is emitted , it would have same direction as that of electron because we need to add negative momentum to make momentum conserved that indicates the direction of electron.

And will have momentum equal to $1.3967\times {10}^{-22}kgm/s$

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