Problem 16.54 Challenge

a) จาก \(E_{0} = m_{0}c^{2}\)

\(E_{0} = (1.67\times 10^{-27} kg)(3.00\times 10^{8} m/s)^{2}(\frac{1.00 eV}{1.60\times 10^{-19} J})\)

\(E_{0} = 939 MeV \;\blacksquare\)

b) จาก \(E = γm_{0}c^{2}\)

\(3E_{0} = \gamma E_{0}\)

\(\gamma = 3\)

\(\gamma ^{2} = 9\)

\(\frac{c^{2}}{c^{2} - v^{2}}= 9\)

\(v =\frac{2 2}{3}c = 0.943c \;\blacksquare\)

c) จาก \(K = E - E_{0}\)

\(K = 3E_{0} - E_{0}\)

\(K = 2E_{0}\)

\(K = 2(939 MeV) = 1.88 GeV \;\blacksquare\)

d) จาก \(E^{2} = p^{2}c^{2} + E_{0}^{2}\)

\((3E_{0})^{2} = p^{2}c^{2} + E_{0}^{2}\)

\(8E_{0}^{2} = p^{2}c^{2}\)

\(p =\frac{2 2E_{0}}{c}\)

\(p =\frac{2 2(939 MeV)}{c}= 2.66 GeV/c \;\blacksquare\)