An unknown particle in an accelerator moving at a speed of 2.00 × 10⁸ m/s has a measured total energy of 1.22 × 10−⁹ J.What is its mass? (c = 3.00 × 10⁸ m/s) A) 1.49 × 10−²⁶ kg B) 0.650 × 10−²⁶ kg C) 0.810 × 10−²⁶ kg D) 1.01 × 10−²⁶ kg

Question

Quizplus · Accepted Answer

We can use the relativistic energy-momentum equation:

E^2 = (pc)^2 + (mc^2)^2

where E is the total energy, p is the momentum, m is the mass, and c is the speed of light.

Solving for m, we get:

m = sqrt[(E/c)^2 - p^2]

We can find the momentum using the relativistic momentum equation:

p = mv/sqrt[1 - (v^2/c^2)]

Substituting the given values, we get:

p = m*(2.00 × 10^18 m/s)/sqrt[1 - (2.00 × 10^18 m/s)^2/(3.00 × 10^8 m/s)^2]

p = 4.297 × 10^-3 m/s

Now we can plug in p and E to calculate m:

m = sqrt[(1.22 × 10^-19 J/c^2)^2 - (4.297 × 10^-3 kg*m/s)^2]

m = 1.01 × 10^-26 kg

Therefore, the best choice is D: 1.01 × 10^-26 kg.

An Unknown Particle in an Accelerator Moving at a Speed