E_{A} = 5 GeV = 8 × 10^{10} J

E_{A} = γ_{A}m_{e}c^{2}

γ_{A} = 9782

\begin{aligned}v_{A} & = c\sqrt{1 − \frac{1}{γ_{A}^{2}}} = c(1 − γ_{A}^{−2})^{1/2} ≃ c(1 − \frac{1}{2}γ_{A}^{−2}) \\ & ≃ c(1 − 5 × 10^{−9}) \end{aligned}

t_{A} = \frac{1.5 × 10^{11} m}{c(1 − 5 × 10^{−9})} = \frac{1.5 × 10^{11} m}{c}(1 − 5 × 10^{−9})^{−1}

≃ \frac{1.5 × 10^{11} m}{c}(1 + 5 × 10^{−9})

≃ 500.4 s (1 + 5 × 10^{−9}) ≃ 500.4 + 2.6 × 10^{−6} s

E_{B} = 10 GeV = 16 × 10^{10} J

E_{B} = γ_{B}m_{e}c^{2}

γ_{B} = 19563

\begin{aligned}v_{B} & = c\sqrt{1 − \frac{1}{γ_{B}^{2}}} = c(1 − γ_{B}^{−2})^{1/2} ≃ c(1 − \frac{1}{2}γ_{B}^{−2}) \\ & ≃ c(1 − 1.3 × 10^{−9}) \end{aligned}

\begin{aligned}t_{B} & = \frac{1.5 × 10^{11} m}{c(1 − 1.3 × 10^{−9})} = \frac{1.5 × 10^{11} m}{c}(1 − 1.3 × 10^{−9})^{−1} \\ & ≃ \frac{1.5 × 10^{11} m}{c}(1 + 1.3 × 10^{−9}) \\ & ≃ 500.4 s (1 + 1.3 × 10^{−9}) ≃ 500.4 + 0.7 × 10^{−6} s \end{aligned} t_{A}−t_{B} = (500.4 + 2.6 × 10^{−6})−(500.4 + 0.7 × 10^{−6}) ≃ 2×10^{−6} s

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