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Chapter 37: Q51P (page 1148)

Question: What must be the momentum of a particle with mass m so that the total energy of the particle is 3.00 times its rest energy?

Short Answer

Expert verified

Answer

The momentum of the particle is 2.83 mc.

Step by step solution

01

Relativistic momentum of a particle.

The relativistic momentum of particle is defined as

p=γmv

Where,γ is the Lorentz factor, mis the rest mass and v is the speed of the particle.

02

Determine Lorentz factor from the given relation.

The given relation is

E=3Eo

Here, E is the total energy and E0 is the rest mass energy.

γmc2=3mc2γ=3

03

Determine speed of the particle from the Lorentz factor 

.

The Lorentz factor is defined in terms of speed is

γ=11-V2/C2vc=1-1γ2

Substitute the values and solve as:

vc=1-132v=0.9428c

Substitute Lorentz factor and speed of the particle in momentum expression and solve as:

p=3m0.9428c=2.83mc

Hence, the momentum of the particle is 2.83 mc .

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