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 × 105 N m-2.

 How much less is the atmospheric pressure than the 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:

E2 = m2c4 + p2c2

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.