- #1
Kavorka
- 95
- 0
Show that Planck's law expressed in terms of the frequency f is:
u(f) = (8πf2/c3)(hf/(ehf/kT - 1))
from the equation:
u(λ) = (8πhcλ-5)/(ehc/λkT - 1)
When I do this algebraically by simply plugging in λ = c/f, I get:
u(f) = (8πhc-4)/(f-5(ehf/kT - 1)
which clearly doesn't involve the correct powers of c and f.
This is the same thing I get when going back and putting n(λ) = 8πλ^-4 in terms of the frequency and multiplying it by the average energy E bar = hf/(ehf/kT - 1) to get u(f).
Going through all of these equations is confusing and I am having trouble putting it all together, but I figure that the problem is I need to go back and differentiate somewhere, since n(λ) is found from n(λ)dλ which involves the range between λ and λ+dλ, but it hasn't been converted to the range between f and f+df. I don't know how I would go about doing any of this...please help!
u(f) = (8πf2/c3)(hf/(ehf/kT - 1))
from the equation:
u(λ) = (8πhcλ-5)/(ehc/λkT - 1)
When I do this algebraically by simply plugging in λ = c/f, I get:
u(f) = (8πhc-4)/(f-5(ehf/kT - 1)
which clearly doesn't involve the correct powers of c and f.
This is the same thing I get when going back and putting n(λ) = 8πλ^-4 in terms of the frequency and multiplying it by the average energy E bar = hf/(ehf/kT - 1) to get u(f).
Going through all of these equations is confusing and I am having trouble putting it all together, but I figure that the problem is I need to go back and differentiate somewhere, since n(λ) is found from n(λ)dλ which involves the range between λ and λ+dλ, but it hasn't been converted to the range between f and f+df. I don't know how I would go about doing any of this...please help!