Planck's Law/ number of photons

[CINA]

Homework Statement

Produce plots of I(λ, T) vs. λ for a blackbody at temperature T = 500 K. Compute the number of photons emitted with 400nm < λ < 450 nm for each temperature, assuming the total surface area is 1.0000 m2, to 5 significant figures.

Homework Equations

Planck's Law
$$A\int_{\lambda_2}^{\lambda_1}I'(\lambda,T)\,d\lambda$$
maybe more

The Attempt at a Solution

I'm having trouble understanding how we are supposed find the number of photons. So far we used n = (P*λ)/hc to find the number of photons at a spefic wavelength. But this requires a specific wavelength. Are we supposed to find the power at 400 nm wavelength, put it into that equation and find n, then move onto the 451, and repeat? Or is there an equation that will compute n number of photons emitted over a wavelength range in one fell swoop?

 

[ehild]

Divide I(λ,T) by the energy of one photon: you get the function N(λ,T), the number of photons emitted. Plot N(λ,T) and find the area between the given wavelengths.

ehild