How fast must an electron move in order for its mass in motion to be twice its rest mass?
September 12, 2021 | education
| The mass of the body “m” moving with the speed “V” is determined by the formula: m = m0 / square root of (1 – V ^ 2 / c ^ 2), where “m0” is the mass of the body at rest, “c” is the speed of light From the formula, it can be seen that a doubling of the mass is possible if the denominator of the formula becomes 0.5: m = m0: 0.5 = 2 * m0 Thus we get: square root of (1 – V ^ 2 / c ^ 2) = 0.5 1 – V ^ 2 / c ^ 2 = 0.5 ^ 2 1 – V ^ 2 / c ^ 2 = 0.25 V ^ 2 / c ^ 2 = 1 – 0.25 V ^ 2 / c ^ 2 = 0.75 V ^ 2 = 0.75 * c ^ 2 V = square root of (0.75 * c ^ 2) V ~ = 0, 87 * c I.e. the electron must accelerate to 0.87 of the speed of light or: V = 0.87 * c = 0.87 * 300’000 [km / s] ~ = 261’000 [km / s]
Answer. 261’000 km / sec.
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