# What is the mass of light 1

## Quantum object photon

#### The light in the photon image

According to Albert EINSTEIN:

When light spreads, the energy is not continuously distributed over space, but is localized in a finite number of energy quanta. Light is a stream of energy packets (photons) that move at the speed of light, are indivisible and can only be generated or absorbed as a whole.

For the energy of a photon, \ [{E _ {{\ rm {Ph}}}} = h \ cdot f \ quad (1) \]

Monochromatic (single-colored) light consists of light quanta of uniform energy.

With the same frequency, more intense light means the occurrence of more light quanta per unit of time, but not the occurrence of higher-energy photons.

Hints

• The pictorial representation of the photons is somewhat problematic. If they are represented as small spheres, one could quickly evoke associations with NEWTON's corpuscles. Here a wave packet was chosen as a representation to remind that the photon energy can be calculated from the frequency of the light.

• The photons were shown here in color in order to be able to distinguish monochromatic light (light of one frequency) from non-monochromatic light.

#### Interpretation of the photo effect

If suitable electromagnetic radiation hits a solid, electrons can be released from its surface. This phenomenon is known as external photo effect (or as an external photoelectric effect).

In the photon image, the photo effect is interpreted as follows: The energy of a photon \ ({E_ {ph}} = h \ cdot f \) can be used to calculate the work WA. to perform and the released electron the kinetic energy Ekin, el granted. According to the energy law, \ [{E_ {ph}} = {W_A} + {E_ {kin, el}} \] or \ [h \ cdot f = {W_A} + {E_ {kin, el}} \; \; \ left (2 \ right) \]

Hints

• The internal photoelectric effect is the phenomenon that in the interior of bodies, into which electromagnetic radiation can penetrate, electrons are detached from atoms and thus the electrical conductivity of the body increases.

• E.kin, el is the maximum possible kinetic energy of the electrons that occurs during the photoelectric effect.

#### Momentum of the photon

With the help of the relation \ (p = \ frac {E} {c} \) from the relativity theory as well as the known relations \ ({{E _ {{\ rm {Ph}}}} = h \ cdot f} \) and \ (\ lambda = \ frac {c} {f} \ Leftrightarrow \ frac {f} {c} = \ frac {1} {\ lambda} \) one obtains for the photon pulse \ [{p _ {{\ rm {Ph} }}} = \ frac {{{E _ {{\ rm {Ph}}}}}} {c} = \ frac {{h \ cdot f}} {c} = \ frac {h} {\ lambda} \ ]

Hints

• If you are interested in the derivation of the formula for the photon momentum, you can display it here.

This means that the rest mass of the photon must be zero.

• You can find more experiments and effects (e.g. Compton effect) on the photon pulse in the link list.

#### Mass of the photon

With the help of the relation \ (E = m \ cdot {c ^ 2} \) from the theory of relativity and the known relation \ ({{E _ {{\ rm {Ph}}}} = h \ cdot f} \) one obtains for the mass of the photon: \ [E = m \ cdot {c ^ 2} \ Leftrightarrow m = \ frac {E} {{{{c ^ 2}}} \ Leftrightarrow {m _ {{\ rm {Ph}}}} = \ frac {{h \ cdot f}} {{{c ^ 2}}} \]

Hints

• As you have already learned from the derivation of the photon pulse, the photons have no rest mass.

• You can find more experiments to confirm the mass of photons in the link list.

#### Energy-momentum relationship in the photon

As was already used in the derivation of the pulse formula for the photon (see above), the following relationship between energy and momentum for the photon applies: \ [{E _ {{\ rm {Ph}}}} = c \ cdot {p _ {{\ rm {Ph}}}} \]