The kinetic energy of a proton is 10 Ge V. Find its momentum and velocity.

Answer

`5.8xx10^(-18)kgm//s;u=betac=0.996c`

Explanation

The total energy is `E = K + E_(0)` = 10.94 GeV. The momentum may be found from the relation
`p=1/csqrt(E^(2)-E_(0)^(2))=1/csqrt(K(2E_(0)+K))=`
`=1/(3.0xx10^(a))sqrt(10xx11.88xx1.6^(2)xx10^(-20))=`
`=(10.9xx1.6xx10^(-19))/(3.0xx10^(8))=5.8xx10^(-18)` kg .m/s
If `KltltE_(0)` one may with sufficient accuracy assume that
`p=K/c=(10xx1.6xx10^(-10))/(3.0xx10^(8))=5.3xx10^(-18)` kg .m/s
The error will be
`e=(5.8-5.3)//5,8 ~~ 5%`
The velocity may be found from the relation
`beta=u/c=(muc)/(mc^(2))=(pc)/e~~K/E=(10.0)/(10.9)=0.92`