Understanding de Broglie formula for massless particles

[outoftown]

I have taken down in my notes that for massless particles the formula by DeBrogle becomes
E = pc, where p is momentum and c is the speed of light.

But what I don't understand is how you can calculate momentum without mass? I thought momentum was mass times velocity? The specific example I am thinking of is photons. Thanks for the help.

 

[Bill_K]

Dear OutOfTown,

The first thing you should do is open your notebook. Where it says "DeBrogle", cross that out and write the man's actual name, "de Broglie". What you need to know is that he was French and has a wavelength named after him. Next, in the margin alongside "E = pc" write, "This formula has nothing to do with Louis de Broglie or quantum mechanics. It comes from special relativity and applies to any massless object."

Momentum is an important concept in mechanics. For a slowly moving particle, p = mv, but that is not its definition. Primarily, momentum is the quantity that enters into Newton's second law of motion, and is conserved, meaning that its total value is the same before and after a collision. For a rapidly moving particle, p = γmv, where m is the rest mass and γ = 1/sqrt(1-v²/c²). People who want to insist that p = mv call γm the relativistic mass, but that is more confusing than it is useful. When you're dealing with particles that are relativistic, rather than talk about v = 0.999 c or v = 0.9999 c, it's much easier to give the particle's momentum.

In general, the relationship between energy and momentum is E = sqrt(p²c² + m²c⁴). For a particle at rest this reduces to E = mc², while for a massless particle it reduces to E = pc.

 

[khemist]

It reduces to e = pc.

from Planck's quantum hypothesis, E = hf

so pc = hf and p = hf/c for a massless particle

 

[Gordon Watson]

Someone needs to fix the spelling of "de Broglie" in the title of this thread.

Otherwise it will be missed in searches.
..

 

[berkeman]

Someone needs to fix the spelling of "de Broglie" in the title of this thread.

Otherwise it will be missed in searches.
..

Done. Thanks Gordon.