How Do You Calculate the Number of Photons from Sunlight on Earth?

[sollinton]

Homework Statement

Light from the sun arrives at the earth, an average of 1.5*10¹¹ m away, at the rate of 1.4*10³ W⁄m² of area perpendicular to the direction of the light. Assume that sunlight is monochromatic with a frequency of 5.0*10¹⁴ Hz.

(a) How many photons fall per second on each square meter of the earth’s surface directly facing the sun?

(b) What is the power output of the sun, and how many photons per second does it emit?

(c) How many photons per cubic meter are there near the earth?

Homework Equations

Here is where I am running into trouble. I do not know any relationships between the data given and the number of photons present. I know the relationship has to do with the frequency of light, but I do not know the exact conversion.

The Attempt at a Solution

So far I have only been able to calculate the power output of the sun (which I found to be 3.592*10²⁶ W. As stated above I do not know how to find the number of photons given the information above, and am not sure that I can proceed without this information.

I have searched around the internet and in my textbooks, but the only equations with photons that I can find are those concerning the photoelectric effect, relating hf to the kinetic energy of electrons.

 

[rock.freak667]

A relevant equation would be that the energy of a photon is hf. (and you know that f=5.0(10¹⁴) Hz.

So 'hf' Joules of energy gives 1 photon

3.592(10²⁶) J in 1 second will give <some number> in 1 second.

EDIT: For the first part, the energy incident 1.4(10³) W/m², so you need to still find the energy of one photon and do the same type of thing.