Photon density in beam of light

[w3390]

Homework Statement

The wavelength of red light emitted by a 5.00 mW helium-neon laser is 633 nm. If the diameter of the laser beam is 1.60 mm, what is the density of photons in the beam? Assume that the intensity is uniformly distributed across the beam.

Homework Equations

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The Attempt at a Solution

I do not even know where to start to attempt this problem because I cannot find a formula that looks helpful for this. Any input on what formula I should use or what approach to take would be greatly appreciated.

 

[kuruman]

A 5 mW laser puts out 5 mJ worth of energy per second. If you find the energy of one photon, you can find how many photons per second the laser puts out. This should get you started.

 

[w3390]

Okay, so I calculated that the energy of one photon is 3.1403e-19 J. So I divided 5mW by 3.1403e-19 J and got 1.578e-21 photons/second. Now to get to photons/cubic meter, I need to get the volume of the path of light. Since I am given the diameter of the light, I can multiply the area of the circle by the length of a piece of the light. However, what do I use as the length to get cubic meters?

 

[kuruman]

Your number 1.578x10^-21 is incorrect. Check your powers of 10.

Assume the correct number of photons per second is N. Then you have N photons in the volume of cylinder whose diameter you have. What is the height of the cylinder? One end (at the laser) has all the photons that were emitted at the end of the the 1-second interval. The other end of the cylinder has all the photons that were emitted at the beginning of the 1-second interval. So the height of the cylinder is ...

 

[w3390]

So I think I found the calculation error in the photons per second. Now I have that there are 1.5922e16 photons/second. Also, since a photon travels at 3e8 m/s, I would multiply the area of the circle (pi*d) by 3e8m to get my volume? However, when I did this, I got 1.056e10 photons/cubic meter and my homework says this is wrong. Any suggestions?

 

[kuruman]

The area of a circle is not πd. That's the circumference. What is the area of a circle?

 

[w3390]

Wow. That was embarrassing. I'm sorry you had to see that. Thanks for your help.