Calculating Visible Light Photons Emitted Per Second & Distance

[EK86017]

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!

 

[berkeman]

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

.

 

[EK86017]

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