# Planck's Law, Quantum mechanics help

1. Oct 13, 2011

### hxcguitar101

1. The problem statement, all variables and given/known data
(2) The orbiting space shuttle moves around the Earth well above 99% of the atmosphere, yet it still accumulates an electric charge on its skin due (in part) to the loss of electrons caused by the photoelectric effect from sunlight. Suppose the skin of the shuttle is coated with nickel for which the work function is φ = 4.87 eV at the temperatures encountered while in orbit. (A) What is the maximum wavelength of solar radiation that can result in electron emission from the shuttle’s skin? (B) What is the maximum fraction of the total power falling on the shuttle that could potentially produce photoelectrons?

I Found the answer to part A to be 255 nm... how do you find part B?

2. Relevant equations

Planks law: u(λ) = 8πhcλ^-5)/(e^(hc/λkT)-1)

3. The attempt at a solution

I set up the integral: Int(8πhcλ^-5)/(e^(hc/λkT)-1)) from 0 to 255nm all over the same integral from 0 to infinity (planck's law) but I have NO IDEA how to solve it! THANKS

Last edited: Oct 13, 2011