An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?

Question

rhondasommer · Answer

okay so its on problem 1. Thats the only way I can help you :/ http://www.cabrillo.edu/~jmccullough/physics4c/files/Solutions/Ch38_example_solutions.PDF

kainui · Answer

Watts is energy per second, and each photon carries a certain amount of energy. Main relations here are:

$$E= h \nu$$ and $$c = \lambda \nu$$ 
The first one says energy of a photon is directly proportional to its frequency  which makes sense cause the more frequently you're oscillating the more energy you must have to do that. The other relation is the speed of light is the distance it travels in one wave divided by the time it takes to make one wave, conveniently distance is rate times time, except the time is written as frequency which makes it look a bit different.

So alright, so power has units of Watts, energy per time, and since energy is dependent on the number of photons and their total energy, 

$$P = \frac{E}{t} = \frac{h \nu n}{t} = \frac{h c}{\lambda} \frac{n}{t}$$

We can then rearrange this to get:

$$\frac{P \lambda}{h c} = \frac{n}{t} = R$$

since n/t is the rate of photons per unit time. We know the power, wavelength, Planck's constant and the speed of light. :D

ganeshie8 · Answer

a photon of the light wave with high frequency will have high energy
so, it takes less photons of high frequency to have the same power ?

kainui · Answer

Yeah exactly right. I think a lot of people get stumped on the frequency vs wavelength thing but if you imagine a little wave, faster oscillations (higher frequency) mean you complete a wave much faster, so the length of a single complete wave is much shorter.

kainui · Answer

Also I realize I just wrote "Watts is energy per second" I meant to say "Watts are Joules per second" for the units. The dimensions of Watts I did say correctly as energy per time a little later but anywho.

ganeshie8 · Answer

ahh alright
power is energy per second

since it takes more photons for the infrared to achieve the same power as ultraviolet.
qualitatively, this means the rate of photons must be `greater for infrared` to achieve the same power as the photons of the ultraviolet

ganeshie8 · Answer

part b can be done with those equations i hope.. let me try..

kainui · Answer

Yeah, makes sense. It's like if you wanna fill your bank account with 5 cent coins or 1 cent coins, you need more 1 cent coins to fill the bank to the same amount of money haha.

ganeshie8 · Answer

Awesome! thanks :)

ganeshie8 · Answer

part b http://www.wolframalpha.com/input/?i=400*700*10^%28-9%29%2F%286.62607004+*10^%28-34%29*299792458%29

ganeshie8 · Answer

agrees w/ the text book answer, thanks again :)

kainui · Answer

Awesome glad I could help. Photons are very strange.