Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Converting between λ and ν for Blackbody Radiation?!

  1. Apr 18, 2016 #1
    Forgive me for this stupid question, but how do I convert between

    b57bebb5337f0de6333ec9bc85688c08.png

    and

    46a1efc581519117de92da6afb5a8e78.png

    I tried c = νλ but that doesn't work. This is the Rayleigh Jeans Law by the way.
     
    Last edited: Apr 18, 2016
  2. jcsd
  3. Apr 18, 2016 #2

    pl. give the full expression of the quoted equation and where these two are being used.
     
  4. Apr 18, 2016 #3
  5. Apr 18, 2016 #4
    The Rayleigh–Jeans law agrees with experimental results at large wavelengths (low frequencies) but strongly disagrees at short wavelengths (high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe,

    see the full expressions
    associated Rayleigh–Jeans limits are given by

    c0313ce746394b13ace2e1e668e6f176.png
    or

    22ed0ae7e400ebb5306a059fb4b69c1f.png
    now you can see the approximations- actually they are not exact expressions
     
  6. Apr 18, 2016 #5
  7. Apr 18, 2016 #6

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    You only have to remember that these are probability distributions ##\mathrm{d} N/\mathrm{d} \nu## or ##\mathrm{d} N/\mathrm{d} \lambda##. Now you have ##\nu=c/\lambda##. This implies
    $$B_{\nu}=\frac{\mathrm{d} N}{\mathrm{d} \nu}=\frac{\mathrm{d} N}{\mathrm{d} \lambda} \left|\frac{\mathrm{d} \lambda}{\mathrm{d} \nu}\right| = B_{\lambda} \frac{c}{\nu^2}.$$
    Now with
    $$B_{\lambda}=\frac{2 c k_B T}{\lambda^4}=\frac{2 k_B T \nu^4}{c^3} \; \Rightarrow\; B_{\nu}=\frac{2 k_B T \nu^2}{c^2},$$
    and this was to be shown.
     
  8. Apr 18, 2016 #7
    Thank you guys.

    For
    b57bebb5337f0de6333ec9bc85688c08.png

    and

    46a1efc581519117de92da6afb5a8e78.png

    the peak intensities occur at different wavelengths or frequencies.


    How do scientists measure the spectral radiance of blackbodies? Are there TWO types of equipment, one for [tex]B_\lambda[/tex] and the other for [tex]B_\nu[/tex], such that each device yields a peak at a different frequency?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Converting between λ and ν for Blackbody Radiation?!
  1. Blackbody Radiation (Replies: 2)

Loading...