Calculate the momentum of a proton whose kinetic energy is 200 MeV.
Given
"E^2 - p^2 c^2 =m^2 c^4" where E is full energy, p is momentum and m - mass,
and
"E = T+E_0 = T+mc^2"
we obtain
"(T+mc^2)^2 - p^2c^2 = m^2 c^4"
"T^2 +2Tmc^2 + m^2c^4 -p^2c^2 =m^2c^4"
"p^2c^2 = T^2 +2Tmc^2"
"pc = \\sqrt{T^2+2Tmc^2}"
Let's calculate all in units of GeV, "T=200\\; MeV , mc^2 =938 \\; MeV".
"pc = \\sqrt{200^2 + 2\\cdot 200 \\cdot 938}=\\sqrt{415\\,200}=644.36 \\; MeV"
Answer: p = 644.36 MeV/c.
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