Quantum Physics Tutorial 7 - Radiation Pressure
Contents |
We know that pressure is defined as force per unit area:
It may be a surprise, but there is a pressure from the photons arriving from the Sun. This is called radiation pressure. Like any other pressure, its units are Pa.
It has a value of about 10 × 10^{-6} Pa, which is not exactly going to crush you. Atmospheric pressure, for comparison, is about 1 × 10^{5} N m^{-2}.
How much less is the atmospheric pressure than the radiation pressure? |
All electromagnetic radiation results in radiation pressure.
When radiation strikes a surface, momentum from the particles is transferred to the surface. The change in momentum leads to a force.
You might (correctly) think that photons have no mass (hence zero momentum), but relativity allows them to have momentum by this general equation:
E^{2} = m^{2}c^{4} + p^{2}c^{2}
This is consistent with mass and energy being equivalent.
When mass is zero, we get the following result:
E = pc
And by rearranging:
Where:
p = momentum (N s);
E = photon energy (J);
c = speed of light (m s^{-1}).
We also know that force is defined as rate of change of momentum (Newton II):
Rearranging:
Dp = FDt
We can combine the two equations above by writing:
And then we write an expression for F:
We can see that there is an energy ÷ time component. This is power, so we can write:
A light source has a power of 6.0 W. What is the force from its photons? |
We know that:
So we can divide the equation above by the area:
Power divided by area gives intensity, so we can write:
where I is the intensity (W m^{-2}).
The intensity of light striking the Earth's surface at a certain spot is 550 W m^{-2}. What is the radiation pressure? |
The wavelength does not matter, because the lower the photon energy, the more photons are needed for a given power.
Note that both pressure and momentum have the same code, p. Make sure you know which context you are using p in. |
Radiation pressure can be used for optical refrigeration which the vibration of atoms can be reduced as they interact with incoming photons from a laser.