How Do Photons Exert Force Without Mass?

[vette982]

If p=E/c for a photon, and I'm given a bunch of other equations such as E=hc/λ and p=h/λ and E=hf and more...

Note: h=planck's constant, f=frequency, c=speed of light, E=energy, p=momentum.

I'm wondering how to find dp/dt (=Force)?Original question:
Photons carry momentum, hence they exert pressure on the surface they strike. In this question, we we'll computer the approximate pressure at a distance r exerted by radiation from a star, using the relativistic equation between energy, momentum, and mass. Pressure is force exerted per unit surface area. The force exerted per particle can be written dp/dt where p is the momentum of the particle (from F ~ v^2 and p ~ v). Derive an expression for pressure P at a radius r from the radiation originating isotropically from a point source (i.e. a star), in terms of the momentum of the photons and radius r. (This is most easily derived by imagining that the photons are striking a spherical shell of radius r centered on the star).

 

[malawi_glenn]

it depends on if the photon is absorbed or totally reflected.

Are you looking for radiation pressure? Use stefan boltzmans law, or rather, derive it.

 

[nlightner]

I would approach this question by first considering the properties of photons and their relationship to force and momentum.
A photon is a massless particle that travels at the speed of light, c. It carries a momentum, p, given by the equation p=E/c, where E is its energy. This can also be expressed as p=h/λ, where h is Planck's constant and λ is the photon's wavelength.
Now, let's consider the force exerted by a single photon on a surface it strikes. From the equation F=ma, we can see that the force exerted by a photon would be very small since it has no mass. Therefore, we can use the equation F=dp/dt, where p is the momentum of the photon and t is the time it takes for the photon to transfer its momentum to the surface.
Since we are considering radiation from a star, we can assume that the photons are originating isotropically from a point source and are striking a spherical shell of radius r centered on the star.
To derive an expression for pressure, P, at a radius r, we can consider the total force exerted by all the photons on the surface of the shell. This can be calculated by integrating the force exerted by each photon over the surface area of the shell.
Therefore, the pressure at a radius r can be expressed as P=∫F/A, where A is the surface area of the shell and F=dp/dt.
Substituting the expression for momentum, p=h/λ, we get P=∫(h/λ)/A dt.
Since we are considering a spherical shell, the surface area can be expressed as A=4πr^2.
Substituting this into the equation, we get P=∫(h/λ)/4πr^2 dt.
Assuming that the photons are striking the shell with a constant frequency, f, we can also express the time it takes for a photon to transfer its momentum as dt=1/f.
Substituting this into the equation, we get P=∫(hf/4πr^2)/λ df.
Using the equation E=hf, we can express this as P=∫(E/4πr^2)/λ df.
Finally, substituting the equation for wavelength, λ=hc/E, we get P=