1.

A stationary neutral particle disintegrated into a proton with kinetic energy `T= 5.3MeV` and a negative pion. Find the mass of that particle. What is its name.

Answer» By conservation of energy-momentum
`Mc^(2)=E_(p)+E_(pi)`
`O=vec(p_(p))+vec(p_(pi))`
Then `m_(pi)^(2)c^(4)=E_(pi)^(2)-vec(p_(pi))c^(2)=(Mc^(2)-E_(p))^(2)-c^(2)vec(P_(p))`
`=M^(2)c^(4)-2MC^(2)E_(p)+m_(p)^(2)c^(4)`
This is a quadratic equation in `M`
`M^(2)-2(E_(p))/(c^(2))M+m_(p)^(2)+m_(pi)^(2)=0`
or using `E_(p)=m_(p)c^(2)+T` and solving
`(M-(E_(p))/(c^(2)))^(2)=(E_(p)^(2))/(c^(4))-m_(p)^(2)+m_(pi)^(2)`
Hence, `M=(E_(p))/(c^(2))+sqrt(m_(pi)^(2)+(T)/(c^(2))(2m_(p)+(T)/(c^(2))))`
From the table of masses we identifiy the particle as a `^^` particle


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