The rest energy of a proton is 938 MeV. If its kinetic energy is also 938 MeV, calculate its momentum and speed.
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Rest energy of proton = RE = m₀ c² = 938 *10⁶ eV
Rest mass = 938 *10⁶ * 1.6 * 10⁻¹⁹ /3² * 10¹⁶ = 1.667 * 10⁻²⁷ kg
KE = 938 MeV = p c
Momentum = p = 5.003 * 10⁻¹⁹ kg-m/s
Energy-momentum relation in relativistic physics:
E² = (m₀ c²)² + (p c)²
Total energy = √2 * 938 eV
speed = u
Lorentz factor = √[1 + (p/m₀ c)² ] = √2
Lorentz factor = √[1 - u²/c² ] = √2 So u = c/√2
OR, u/c = p / [√2 m₀ c ] = 1/√2 as p = m₀ c in this case
u = speed = c/√2 = 2.12 * 10⁸ m/s
Rest mass = 938 *10⁶ * 1.6 * 10⁻¹⁹ /3² * 10¹⁶ = 1.667 * 10⁻²⁷ kg
KE = 938 MeV = p c
Momentum = p = 5.003 * 10⁻¹⁹ kg-m/s
Energy-momentum relation in relativistic physics:
E² = (m₀ c²)² + (p c)²
Total energy = √2 * 938 eV
speed = u
Lorentz factor = √[1 + (p/m₀ c)² ] = √2
Lorentz factor = √[1 - u²/c² ] = √2 So u = c/√2
OR, u/c = p / [√2 m₀ c ] = 1/√2 as p = m₀ c in this case
u = speed = c/√2 = 2.12 * 10⁸ m/s
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