If a proton with mass 1.67 × 10−²⁷ kg moves in an accelerator such that its total energy is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s) A)2.83 × 10⁸ m/s B)2.45 × 10⁸ m/s C)2.00 × 10⁸ m/s D)1.00 × 10⁸ m/s E)1.54 × 10⁸ m/s

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Quizplus · Accepted Answer

The total energy (E) is given as three times the rest energy (E₀), so E = 3E₀. According to the theory of relativity, E = γE₀, where γ = 1 / sqrt(1 - v²/c²). Setting 3E₀ = γE₀ and solving for v, we find that v = sqrt(8/9)c. Substituting c = 3.00 × 10^8 m/s gives v ≈ 2.83 × 10^8 m/s.

If a Proton with Mass 1