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Plank's law - my computer is having trouble with the formula

  1. Apr 3, 2007 #1

    tony873004

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    Plank's law -- my computer is having trouble with the formula

    [tex]f_\lambda \left( T \right) = \frac{{2\pi hc^2 /\lambda ^5 }}{{\exp \left( {\frac{{hc}}{{\lambda kT}}} \right) - 1}}
    [/tex]

    I'm guessing this thing wants wavelength in meters. So for a temperature of 5600 K and a wavelength of 0.5 um (5e-7 m), the part that I'm using as the exponent for e, [tex]{\frac{{hc}}{{\lambda kT}}}
    [/tex] comes out to (6.626068e-24*2.99792458e8/(5e-7*1.3806503e-23*5600)) =51384823425.8871.

    And e^51384823425.8871 is not a number my computer can calculate.

    How can I use this formula?
     
  2. jcsd
  3. Apr 3, 2007 #2
    Not a complete solution- but worth trying.
    ln(f(T))=ln(2pi h c^2/lambda^5)-hc/lambda k T

    Accurate to a lot of sig. fig.

    Compare the magnitude of the two terms on the RHS to see if one dominates by orders of magnitude.
     
  4. Apr 3, 2007 #3

    tony873004

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    Thanks. Someone in the math department at school recommended the same thing. However, my value for plank's constant turns out to be wrong. I must have made a typo. it's e-34, not e-24. This turns the value fed to exp( ) from5.138e10 into a managable 5.138.

    Thanks for your reply.
     
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