The maximum wavelength of light emitted from a blackbody that will emit electrons from a given piece of metal is 255nm. What is the fraction of total energy emitted from the black body that emits electrons?

Question

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

Answer 1

They are asking for the fraction of the blackbody radiation that has a wavelength less than 255 nm.

This can only be computed if you already know the TEMPERATURE of the blackbody.

Setting up the integral is the right way to go about answering the question, but you still need the temperature.

Answer 2

Here is how it is phased in the question:

(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 part A to be 255nm. But how do you find the temperature from that information?