A fast-moving muon decays in 2 *10 ^- ⁴ seconds, as measured by an observer at rest.In the reference frame of the muon itself, its lifetime is in fact only 2 *10 ^- ⁶ seconds.What is the muon's speed?

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Quizplus · Accepted Answer

The correct answer is E.The muon's speed can be calculated using the time dilation formula:```t' = t / γ```where:* t' is the time measured in the muon's reference frame* t is the time measured in the observer's reference frame* γ is the Lorentz factorIn this case, t' = 2 × 10^-6 s and t = 2 × 10^-4 s. Substituting these values into the formula, we get:```2 × 10^-6 s = 2 × 10^-4 s / γ```Solving for γ, we get:```γ = 100```The Lorentz factor is related to the speed of the muon by the following equation:```γ = 1 / sqrt(1 - v^2/c^2)```where:* v is the speed of the muon* c is the speed of lightSubstituting γ = 100 into this equation, we get:```100 = 1 / sqrt(1 - v^2/c^2)```Solving for v, we get:```v = 0.99995c```Therefore, the muon's speed is 0.99995c.

A Fast-Moving Muon Decays in 2 *10 - 4 Seconds

A Fast-Moving Muon Decays in 2 *10 ^- ⁴ Seconds