Calculate the ratio of the relativistic kinetic energy to the classical kinetic energy, KE_rel/KE_class, for an electron (mass = 9.109 × 10^-³¹ kg) moving with a constant speed of 0.75c.

Question

Quizplus · Accepted Answer

The relativistic kinetic energy for an object with mass m and velocity v is given by:

K_rel = [(γ - 1) * m * c^2]

where γ = [1 - (v/c)^2]^(-1/2) is the Lorentz factor and c is the speed of light.

The classical kinetic energy is given by:

K_class = (1/2) * m * v^2

For an electron with mass m = 9.109 × 10^-31 kg and speed v = 0.75c, we have:

γ = [1 - (0.75)^2]^(-1/2) = 1.5

K_rel = [(1.5 - 1) * 9.109 × 10^-31 kg * (3.00 × 10^8 m/s)^2] = 1.293 × 10^-13 J

K_class = (1/2) * 9.109 × 10^-31 kg * (0.75c)^2 = 2.045 × 10^-14 J

Therefore, the ratio of K_rel/K_class is:

K_rel/K_class = (1.293 × 10^-13 J) / (2.045 × 10^-14 J) ≈ 1.8

So, the correct answer is A) 1.8.

Calculate the Ratio of the Relativistic Kinetic Energy to the Classical