A few questions about photons? (advanced)

[From: ] [author: ] [Date: 11-12-13] [Hit: ]

E = hf, but E = mc^2 as well. Therefore the equivalent mass of a photon is given by mc^2 = hf.Furthermore, f = c/λ (c = speed of light, λ = wavelength)So mc^2 = hc/λContinuing,......

They're (energy and frequency) related by this equation: E = hf.

h is a constant of proportionality called Planck's constant, after the scientist Max Planck (research his work).

As for photons having momentum, consider this. E = hf, but E = mc^2 as well. Therefore the equivalent 'mass' of a photon is given by mc^2 = hf.

Furthermore, f = c/λ (c = speed of light, λ = wavelength)
So mc^2 = hc/λ

Continuing, we end up with λ = h/mc. Remember, momentum is the product of mass and velocity. Velocity in this case is c, the speed of light; the equation becomes λ = h/p. (p = momentum)

Note that the equation λ = h/p holds true for most forms of matter, not just photons.

Hopefully the above answers your first two questions.

I must admit I'm not quite sure how to explain your third question. What you're asking is beyond the scope of my current course of study. I'm sure someone who's a bit more qualified will help you out soon enough. Anyway, physics is awesome! Keep at it.

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1. Momentum is part of the energy of a particle, the part due to its motion through space. It is not intrinsically connected with mass, although p=mv is its most common formulation in basic physics. Massless particles such as photons do move and therefore do have energy associated with their motion and therefore have momentum.

2. It does have momentum so the question makes no sense.

3. E=mc^2 is not a valid equation for massless particles since it is simply an expression of the equivalence of mass and energy. You need to use E^2=(pc)^2+(mc^2)^2 which holds for all particules, including massless onces where you simply get E^2=(pc)^2 or E=pc,

This finally gives you an expression for the momentum of a massless particle p=E/c or (since E=hf) p=hf/c

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