I have just started basic quantum mechanics and have come across this expression for energy density of blackbody radiations; Planck's formulation. $$ u_{\nu} \ d\nu = g(\nu) \ \langle E \rangle \ d\nu $$

The textbook says that:

To model the absorption and emission of electromagnetic radiation by these oscillators, he argued that the spectral energy density of the black body radiation over a range of frequency dv is nothing but the product of the number of oscillators having a frequency between v and v + dv , g(v) and the average energy ⟨E⟩, of an oscillator having a frequency v :

What I don't understand is: if u(v) is the energy density (per unit v), isn't $u(\nu)\ d\nu$ the total energy instead of energy density? And one more question; if $g(\nu)$ is the number of oscillators having frequency in the range $d\nu$, and $⟨E⟩$ is the average energy; then isn't their product the total energy instead of being the energy density, and if that is supposed to be so then why do we have a $d\nu$ part on the right side of equation also?


1 Answer 1


$g(\nu)$ would be the number density of oscillators per unit frequency at a frequency $\nu$.

$u(\nu)\ d\nu$ would be the energy density in a frequency band $d\nu$ at a frequency $\nu$.

The $d\nu$ is written on both sides of the equation since otherwise you are saying $0 = 0$, because no oscillators have a frequency of exactly $\nu$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.