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Energy and Mass with some photons thrown in


zeig

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lol okay this just kills me..Photons are massless energy right? but mass is energy and energy is mass from what i have been taught..so when light hits you, it should have mass and if its traveling at the speed of light wouldn't it just shred us up or create so much thermal energy through friction in the air that we would just like combust?

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The amount of energy and momentum in a single photon is extremely small. The rate at which the electromagnetic energy around you is actually hitting you, is somewhere around 400 watts. (but you actually emit around 500 watts), which is a little over a microNewton of force, distributed all over your body, for perhaps a microPascal of pressure.

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Almost:

[math]p=\frac{h}{\lambda}=\frac{hf}{c}[/math]

I know you know, just correcting your typo :P.

 

*coughs innocently*

 

*waves his hand in a jedi like fashion* "This never happened, the formula was correct"

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Mass is energy...

Yep.

... and energy is mass.

Nope, unless you define mass to be energy (-> relativistic mass) which is kind of silly because you could as well call it energy, then.

 

It's a bit like a dog and an animal. A dog is an animal but an animal doesn't have to be a dog. Kinetic energy is energy. Potential energy is energy. Mass is energy. But the reverse statement that energy is kinetic energy does not need to be true. Same with potential energy. Same with mass.

 

Mass is a form of energy; you might think of it as a form of potential energy for calculational purposes. Even better, more precise and less prone to making errors: Mass is a term that contributes (or at least can contribute) to the energy of a system.

 

Therefore...

 

When light hits you, it should have mass ...

Energy, not mass. In this case, none of the energy comes from mass; it's purely kinetic energy.

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The amount of energy and momentum in a single photon is extremely small.
Well there are clearly a lot. The energy of sunlight is about 1 kilowatt per meter square.

 

Energy, not mass. In this case, none of the energy comes from mass; it's purely kinetic energy.
I'm sure I've read somewhere that kinetic energy can be converted to mass, but I'm too lazy to look it up again the for the correct way of doing that.
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Well there are clearly a lot. The energy of sunlight is about 1 kilowatt per meter square.

 

That just means the photon density is massive!

 

If you consider that 1photon has a wavelenth of about 550nm, that gives you an energy of:

 

3.416182*10-19J

 

So that is about 1022 photons/second/meter square.

 

I'm sure I've read somewhere that kinetic energy can be converted to mass, but I'm too lazy to look it up again the for the correct way of doing that.

 

E2 = (mc2)2 + (pc)2

 

Energy can be converted into mass and vis versa, no one is saying otherwise.

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Well there are clearly a lot. The energy of sunlight is about 1 kilowatt per meter square.

 

Klaynos has pointed out that that means there are a lot of photons. The 1 kW/m^2 number doesn't contradict the 400 W value I gave, either, even though I was thinking of ambient conditions, rather than direct sunlight. You have to remember that humans are a source of thermal photons, too.

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Well there are clearly a lot. The energy of sunlight is about 1 kilowatt per meter square.
A really quick order of magnitude calculation I did (hopefully without a mistake, and just to keep my brain working!) shows that: given 700nm light, and 1kWm-2, then the impulse in that meter square, over 1 second was, per photon: 5*10-40Nm-1 and given that there's 4*1021 photons/sec in 1kW, impulse per m²: 2*10-18Nm-1. Saying the Earth is a disk of radius 6400km, gives a surface area facing the sun of: 1014m2.

 

So a total force on the Earth due to the photons from the sun hitting it is about: 2*10-4N.

 

However this doesn't account for the "counterbalance" of the Earth emitting photons. I was about to say that the dark and light side of the Earth balance each other out, but possibly the light side of the Earth would emit more photons, as it is in the light, thus increasing the force on the Earth due to all photon activity. However it should be a very small effect, even relative to the force I just calculated.

 

 

[edit] wow, took me 15mins to type that, as Klay's post wasn't there when I stared!

Klay: should be 1021 photons per kW, with both mine and your wavelength values. And about those wavelength values, I just chose 700nm as it's a little before green, and I was aiming for the middle of the visible light spectrum. Why did you chose 550nm, which looks like IR to me? Is sunlight mainly IR?

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[edit] wow, took me 15mins to type that, as Klay's post wasn't there when I stared!

Klay: should be 1021 photons per kW, with both mine and your wavelength values. And about those wavelength values, I just chose 700nm as it's a little before green, and I was aiming for the middle of the visible light spectrum. Why did you chose 550nm, which looks like IR to me? Is sunlight mainly IR?

 

550 is green, 700 is red. 550 is in the middle of the spectrum (555 nm is the wavelength where the eye is most sensitive)

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550 is green, 700 is red. 550 is in the middle of the spectrum (555 nm is the wavelength where the eye is most sensitive)

 

Is why I chose 550nm, you soon learn working with optics to default to it...

 

Ah an order out, I was just doing it quickly I started off with 23 then rethought it to 22, thanks ;)

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