The radiometer was invented by Sir William Crookes in 1873 it consists of a rotor with four vanes contained in a partially evacuated glass bulb. The four metal vanes have a shiny reflective surface on one face, and a black light absorbing surface on the opposite side. When the radiometer is exposed to light the radiometer rotor rotates. Many authors, including Einstein worked on a quantitative explanation of the radiometer behavior.
How does the radiometer work
When the radiometer is exposed to light the vanes are subjected to a continuous bombardment both by photons (the quanta of light), and by the molecules of the gas contained in the bulb.
The shiny side: photons bounce off the shiny side of the vane transferring (almost) twice their momentum, and almost no energy. Think of a pin-pong ball colliding with a bowling ball. Similarly the recoiling atoms of the vane provide the momentum for the reflected photon without acquiring much energy.
The average of the sum of all momentum transfers over time is equivalent to a pressure exerted by the radiation.
The blackened side: Photons are absorbed by the blackened side of the vane transferring their momentum and their energy to the vane. The net effect is that a (smaller) pressure is exerted by the radiation, and that the deposition of the photon energy on this side of the vane raises its temperature.
The mill rotates with the shiny side toward the incoming light,
therefore the radiation pressure, although it exists, does not explain
the behavior of the radiometer.
Gas molecules bounce off the atoms of the vane, the energy of the reflected molecule depends on the velocity and direction of the individual target atom in the vane.
The blackened side of the vane is hotter than the shiny side, that is, the atoms on the blackened have a higher average velocity. When a gas molecule impinges on them it receives on the average a bigger “kick” than the average “kick” from the shiny side. The recoil from these “kicks” pushes on the blackened side of the vanes and is responsible for the observed rotation.