Calculating Visible Light Photons Emitted Per Second & Distance

AI Thread Summary
A 200 W light bulb emits approximately 6.03 x 10^19 visible-light photons per second when 10% of its power is converted to visible light. The user is attempting to determine the distance at which this emission corresponds to 1 x 10^11 photons per square centimeter per second. They initially calculated the area incorrectly using A = πr^2 instead of the correct formula for the surface area of a sphere, which is 4πr^2. After receiving clarification, they realized the need to use the correct surface area formula to find the radius. This adjustment will help accurately calculate the distance for the desired photon density.
EK86017
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a.) If the average frequency emitted by a 200 W light bulb is 5x10^14, and 10.0% of the input power is emitted as visible light, approximately how many visible-light photons are emitted per second?

I solved this part of the problem by finding the energy (E = hf) and dividing 10% of 200W by the amount of energy per photon to get 6.03 x 10^19 photons per second.

b. At what distance would this correspond to 1x10^11 visible-light photons per square centimeter per second if the light is emitted uniformly in all directions?

I am stuck on this part of the problem. I tried dividing 6.03 x 10^19 by 1x10^11 to get the how many square centimeters would correspond to 1x10^11 photons per square centimeter per second. I got 6.04x10^8 cm^2. Because the light is emitted uniformly in all directions, I did A = pi*r^2, using the value 6.04x10^8 as "A". I got r = 138.7 m, but this is incorrect.

The problem I think I am having is A = pi*r^2 does not correspond to visible-light in the 3rd dimension, but I am confused as to why the question then does not ask "per CUBIC centimeter?"

Any suggestions would be very much appreciated.
Thanks!
 
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EK86017 said:
a.) If the average frequency emitted by a 200 W light bulb is 5x10^14, and 10.0% of the input power is emitted as visible light, approximately how many visible-light photons are emitted per second?

I solved this part of the problem by finding the energy (E = hf) and dividing 10% of 200W by the amount of energy per photon to get 6.03 x 10^19 photons per second.

b. At what distance would this correspond to 1x10^11 visible-light photons per square centimeter per second if the light is emitted uniformly in all directions?

I am stuck on this part of the problem. I tried dividing 6.03 x 10^19 by 1x10^11 to get the how many square centimeters would correspond to 1x10^11 photons per square centimeter per second. I got 6.04x10^8 cm^2. Because the light is emitted uniformly in all directions, I did A = pi*r^2, using the value 6.04x10^8 as "A". I got r = 138.7 m, but this is incorrect.

The problem I think I am having is A = pi*r^2 does not correspond to visible-light in the 3rd dimension, but I am confused as to why the question then does not ask "per CUBIC centimeter?"

Any suggestions would be very much appreciated.
Thanks!

Welcome to the PF. The surface area of a sphere is not PI * R^2...

http://www.teacherschoice.com.au/Maths_Library/Area and SA/area_2.htm

.
 
Thank you! It worked with 4pi*r^2
 

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