Question

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?

Answer 1

L₀ = 15.12 fermi

Step-by-step 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