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16 December, 12:48

The proton from the decay of the neutron is moving at 0.75 c. An observer on the proton measures the radius of the electron as 10 fermi. A Fermi is 10-15 m. What is the radius of the electron measured by someone on the electron?

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  1. 16 December, 15:12
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    L₀ = 15.12 fermi

    Explanation:

    From Einstein's special theory of relativity's consequence of length contraction, we know that:

    L₀ = L √ (1 - v²/c²)

    where,

    L₀ = Length of the object (electron) measured by observer at rest = ?

    L = Length of the object (electron) measured by observer in relative motion

    L = 10 fermi

    v = relative speed = 0.75 c

    c = speed of light

    Therefore,

    10 fermi = L₀√ (1 - 0.75²c²/c²)

    10 fermi = L₀√ (1 - 0.5625)

    10 fermi = L₀√0.4375

    10 fermi/0.66 = L₀

    L₀ = 15.12 fermi
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