If the total energy of an electron in an accelerator is four times its rest energy,what is its speed? (c = 3.00 x 10⁸ m/s) A)1.98 x 10⁸ m/s B)2.32 x 10⁸ m/s C)2.90 x 10⁸ m/s D)2.99 x 10⁸ m/s

Question

Quizplus · Accepted Answer

The total energy of an electron can be written as: 
E = γmc^2 
where γ is the Lorentz factor and m is the rest mass of the electron. 
We are given that E = 4mc^2, so we can write: 
4mc^2 = γmc^2 
γ = 4

The Lorentz factor can be related to the speed of the electron by: 
γ = 1/√(1 - v^2/c^2) 
where v is the speed of the electron. 
Substituting γ = 4, we get: 
4 = 1/√(1 - v^2/c^2) 
16 = 1 - v^2/c^2 
v^2/c^2 = 1 - 1/16 
v^2/c^2 = 15/16 
v/c = √(15/16) 
v = c√(15/16)

Substituting the value of c = 3.00 x 10^8 m/s, we get: 
v = 2.90 x 10^8 m/s

Therefore, the answer is (C).

If the Total Energy of an Electron in an Accelerator