What is the total energy of a proton moving at a speed of 2.4 × 10⁸ m/s? (proton mass is 1.67 × 10−²⁷ kg and c = 3.00 × 10⁸ m/s) A)1.91E-10 J B)1.77E-10 J C)2.51E-10 J D)2.44E-10 J E)9.02E-11 J

Question

Quizplus · Accepted Answer

The total energy of a proton can be calculated using the relativistic formula:

E = (gamma)mc^2

where gamma (γ) is the Lorentz factor:

gamma = 1 / sqrt(1 - v^2/c^2)

and m is the mass of the proton.

Plugging in the values, we get:

gamma = 1 / sqrt(1 - (2.4 x 10^8)^2/(3.00 x 10^8)^2) = 2.50

E = (2.50)(1.67 x 10^-27 kg)(3.00 x 10^8 m/s)^2 = 2.51 x 10^-10 J

Therefore, the correct answer is C.

What Is the Total Energy of a Proton Moving at a Speed