Problem 15.7

Please wait for the animation to completely load.

The graph represents energy density per wavelength emitted from a hot object versus the wavelength of that light.  You can change the temperature of the object (with the slider) and the value of the maximum wavelength.  Restart.

Starting with the distribution of particles as a function of energy for blackbody radiation (see Section 15.4) below: n(ε)dε = (8Vπ/h3c3) ε2dε /(exp(ε/kBT) − 1).  Rewrite the expression as a function of λn(λ)dλ, where ε = hc/λ.  The plot above is a plot of the energy per volume as a function of λ, called an energy density given by ε(λ)/V = ε n(λ) dλ/V.  The peak of the curve is the wavelength where d(ε(λ)/V)/dλ = 0.

Find an expression for the wavelength where the energy density is a maximum (for a given temperature) and verify it using the animation.