What is the difference in energy between a beta particle at rest and one traveling 0.35c?

They have a difference in energy of 35 eV.

Explanation:

The energy at rest of a particle is given by:

  (1)

Where is the mass of the particle at rest and c is the speed of light.

Beta particles are high energy and high velocity electrons or positrons ejected from the nucleus of an atom as a consequence of a radioactive decay. Either if the beta particle is an electron¹ or a positron² it will have the same mass.

Hence, the mass of the beta particle at rest in equation (1) will be equal to the mass of an electron:

Replacing the values of and c in equation (1) it is gotten:

But , therefore:

It is better to express the rest energy in electronvolts (eV):

⇒

So the energy of the beta particle at rest is 511.875 eV.

Case for the one traveling at 0.35c:

Since it is traveling at 35% of the speed of light it is necessary to express equation (1) in a relativistic way, that can be done adding the Lorentz factor to it:

  (2)

Where v is the velocity of the particle (for this case 0.35c).

The difference in energy between the two particles can be determined using the relativistic form of the kinetic energy:

 (3)

Where E is the energy of the particle traveling at 0.35c and is the energy of the beta particle at rest.

They have a difference in energy of 35 eV.

Key terms:

¹Electron: Fundamental particle of negative electric charge.

²Positron: Is an electron with positive electric charge (similar to an electron in all its properties except in electric charge and magnetic moment).

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table