A proton has a total energy of 2.5 * 10-10 J. How fast is it moving? (M = 1.67 * 10-27 kg)
A)0.90 c
B)0.80 c
C)0.70 c
D)0.60 c
E)0.40 c

Question

Quizplus · Accepted Answer

We can use the equation for total energy of a particle: E = γmc², where γ is the Lorentz factor, m is the mass of the particle, and c is the speed of light.

Rearranging the equation, we have:

γ = E/(mc²)

Plugging in the values, we get:

γ = (2.5 x 10⁹ J)/(1.67 x 10⁻²⁷ kg x (3 x 10⁸ m/s)²)
γ ≈ 3.22

Now, we can use the formula for the Lorentz factor:

γ = 1/√(1 - (v/c)²)

Solving for v/c, we get:

v/c = √(1 - 1/γ²)
v/c = √(1 - 1/10.4)
v/c ≈ 0.8

Therefore, the proton is moving at 0.8 times the speed of light. The correct answer is B).

A Proton Has a Total Energy of 2