About this video
This short video explains that light has momentum even though it has no mass. The familiar p = mv does not work for things moving at the speed of light; special relativity provides a loophole letting massless objects carry momentum. The momentum of a photon is p = h/lambda, where h is Planck's constant and lambda is the wavelength in meters, and this tiny momentum is what could push a solar sail.
You'll be able to
- explain why p = mv cannot be used for a photon.
- use p = h/lambda to describe a photon's momentum.
- state that the wavelength must be in meters when using the formula.
- give an example (a solar sail) that relies on light's momentum.
Key words
- momentum of a photon
- The momentum carried by light, equal to h divided by the wavelength (p = h/lambda).
- rest mass
- The mass an object has at rest; light has none, yet it still has momentum.
- solar sail
- A large sail pushed forward by the momentum of light bouncing off it.
Transcript
- [Narrator] A while back, I was teaching physics in California. I got to class and I was all like, hey class, you wanna 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. Shoulda went to the beach today.
Dude, really? Totally lame. But wait, doesn't light really have mass? It should. It's got momentum so it's gotta have mass. It has 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 wanna 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. Alright, 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 34 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 gonna 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. (ambient techno music)
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.