Photon Momentum | Quantum physics | Physics | Khan Academy

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A while back I was teaching physics in California. I got to class and I was all like, "Hey class, you want to hear a physics joke?"

"Yeah, okay totally!"

"Does light hold mass?"

"I don't know, does it?"

"No, it's not even Catholic!"

Oh man, she should have went to the beach. Really totally lame.

But wait, doesn't light really have mass? It should! It's called momentum, so it's gotta have mass. It adds momentum, so it must have mass.

Whoa! Hey everyone, just calm the heck down! You see, the worst part of all this wasn't that my joke bombed; it was that I actually managed to confuse people by telling it.

My students had read that light has momentum, and they were right! Light really does have momentum. But then I come to class and I'm all like, "Hey guess what? Light has no mass!"

Now my students are thinking to themselves, "Dude, but p equals mv!" In other words, if momentum equals mass times velocity, how could light, which has no mass, ever have momentum?

Well, I had to break it to my students that p equals mv isn't really accurate for things that travel close to the speed of light. For things going that fast, you have to use special relativity.

I don't want to waste a lot of time talking about special relativity in this video, so you're just gonna have to take my word for it that the rules of special relativity allow for a loophole.

This loophole provides a way for massless objects to have momentum.

All right, so the bad news is that we cannot use p equals mv to find the momentum of a photon. The good news is that the formula for the momentum of a photon is simple: the momentum of a photon equals h over lambda.

h is Planck's constant, 6.626 times 10 to the negative 34th joule seconds.

Lambda is the wavelength of the light in meters. Be careful, don't use nanometers. You have to convert to meters.

The momentum of a single photon is going to be extremely small. That's why it doesn't feel like we're getting pushed on very much when light shines on us.

But theoretically, if you had a big enough solar sail, the light bouncing off of that solar sail could propel it forward due to the impulse imparted by the momentum of the light.

Okay, so very long story short, you should never ever use p equals mv to find the momentum of a photon. To find the momentum of a photon, you should always use momentum equals h over lambda.