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

• tony873004

#### tony873004

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

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

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, $${\frac{{hc}}{{\lambda kT}}}$$ 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?

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.

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.