This question deals with phenomenon of the "ultraviolet catastrophe".
a. first, sketch the intensity profile (i. e. intensity vs. wavelength or frequency) and then add the curve that denotes the classical result ("ultraviolet catastrophe"). label both curves on your plot and both axes.
b. as mcquarrie states, "we should expect the nonclassical planck distribution to go over to the classical rayleigh-jeansdistribution at low frequencies, where δe --> 0. show that equation 2 reduces to equation 1 as ν --> 0."
equation 2: dρ(ν, t) = ρν(t)dν = ((8πh)/c3) × ((ν3dν)/(e(hν/kbt) -1))
equation 1: dρ(ν, t) = ρν(t)dν = ((8πkbt)/c3) × ν2dν
- make use of:
- series expansion for ex
- a simplifying assumption for small values of x. (to show that this assumption is valid, calculate the factor hν/kbt at 100k at frequencies of radio waves and ultraviolet radiation.
c. put the idea that it is to picture the functions to see how it leads us to a better fir with the data.
- on the first plot, draw x2 for all positive values of x. this plot shall resemble the classical result.
- on a seperate plot, sketch the form of x3/(ecx -1). assume that c is a positive (nonzero) constant.