Physics Puzzle: Crooke’s Radiometer
Here’s a riddle about a well known object known as Crooke’s radiometer. This is a glass “bulb”-like object with four plates fitted on a metal rod, free to rotate (much like a horizontal windmill). Each plate has a black side and a silver side, as is evident from the photo:
The inside of the bulb is kept at a perfect vacuum. Here’s the riddle: what will happen when the radiometer is placed in direct sunlight?
Scientist X argues that the plates will rotate clockwise, i.e., the silver side of the plates will face the positive rotation angle, because the black side will absorb photons, and hence momentum from light, which will “push it forwards”, like blowing wind on it.
Is scientist X correct?
What will happen as air is slowly (slowly!) let into the vacuum?
Good luck & enjoy!
HINT (ADDED 19/4/2008):
You can order radiometers from science toy stores. Buy one and try it out! Which way does it turn? Is it similar to the situation described in this question? (Hint: “our” radiometer is kept at a perfect vacuum. What mechanisms can turn the plates other than light pressure? Can you estimate the pressure, by the way?)
ANOTHER HINT (ADDED 25/4/2008):
When kept in perfect vacuum, the ONLY interaction of the radiometer’s plates can be via radiation.
When not in perfect vacuum, you will need to be able to estimate which effect is greater: the photon pressure, or the molecule pressure. Can you estimate for what density of air molecules do the two effects become equal in magnitude?
X is not correct. Absorbed photons impart only half the momentum that reflected photons impart. So the dark sides will face the positive rotation angle.
Oh, and as air is slowly let in, the effects of the gassy kinetics will start to overcome the effects of radiation pressure. A radiometer with a partial vacuum turns with the light faces in the positve rotation angle. As gas is let in, the radiometer will come to a stop, then start spinning in the other direction.
Indeed, in perfect vacuum the radiometer will rotate with the dark sides facing in the direction of rotation. This will be reversed as gas is slowly let into the radiometer, as the comment above has noted, but can you guess why?