Energy - Structure of matter

Question 1

What equation is used to give the total energy of a particle?

Answer 1

The total energy, E, of a particle (or of a system of particles) in a force field is given by

• A sum of its resting energy E_0,
• Kinetic energy E_k, and
• Potential energy E_p.

E = E₀+E_k+E_p

Where E₀ is the energy related to the particle mass by the well known Einsteins relationship:

E₀ = m₀c²

• c is the velocity of light in a vacuum
• m is the mass

Question 2

How is the relationship between energy, velocity of movement, and momentum represented for particles with non-zero mass?

Answer 2

For particles with non-zero mass, m>0:

• Energy, E
• Velocity of movement, v
• Momentum, p

are related by equation

E² = m²₀c⁴ + p²c²

Photon, which possesses zero mass also have their rest energy = 0.

Photons do not exist at rest and they move thoughout the system of coordinates by the velocity, c.

Question 3

Describe kinetic energy and the equations related to it.

Answer 3

The kinetic energy E_k is defined by the equation:

E_k = (mv²)/2 = p²/(2m).

Kinetic energy may posses only +ve or zero values.

The potential energy, E_p, of a particle or body moving without any acceleration in a central field of forces of Newton’s type (i.e. in which the force is inversely proportional to the squared distance e.g. Coulomb law, Netwon law of gravity), equals in its absolute value the kinetic energy multiplied by factor 2 but with an opposite sign,

E_p = -2E_k

Therefore, the potential energy is -ve and is equal to the work, which has to be done to remove the particle (body, electric charge), which is attracted, to the distance where the force interaction is negligible.

Zero level of potential energy is thus at distance of ‘infinity’ from the body which creates the field of force.

The choice of the zero-value level of potential energy particularly depends its +ve or -ve value. In the mechanics of mass point we have enountered another equation for the potential energy:

E_p = mgh

• m = mass
• g = gravity acceleration
• h = heigh

In this case, the zero energy level was defined at the surface of the Earth and at the height, h, the potential energy equals the product, mgh.

Question 4

In what units is energy expressed in this context?

Answer 4

The energy is expressed in joules.

However, in atomic physics and in physics of radiation this unit is not suitable and energy is mostly expressed in electronvolts (eV).

1 eV is an energy gained by an electron accelerated by the potential difference of 1 volt.

Since

1J = 1C.1V

and the charge 1C equals the total charge of about 6.10¹⁸ electrons,

1eV = 1.6*10^-19J.

In the physics of elementary particles, the unit eV is also applied as a unit for mass thanks to the equation based on this relationship,

• The rest mass of electron m_e = 0.51 MeV
• Mass of proton m_p = 938.28 MeV
• Mass of neuron m_n = 939.57 MeV