# What truly is spectral blackbody emissive power?

I read that a blackbody at a temperature T, would emit thermal energy in the form of Electromagnetic waves. This thermal energy emitted per unit the area per unit time is called blackbody emissive power and is due to all possible wavelengths.

I then started with this term "spectral blackbody emissive power" which is the amount of thermal energy emitted in the form of EM waves of a particular wavelength, per unit area per unit time and per unit differential change in wavelength. I am not getting what's that differential change in wavelength.

You can't sensibly talk about the power emitted per unit area at a single wavelength, $$\lambda$$, because at that one particular wavelength, no power will be emitted. Even a laser, commonly said to emit monochromatic light, emits over a narrow band of wavelengths, so since that band can be infinitely sub-divided, at any one discrete wavelength, zero power is emitted.
So we consider a very narrow band, $$\Delta \lambda$$, of wavelengths that is centred on $$\lambda$$. A finite amount of power, $$\Delta P$$, will be emitted in this band. But, the power will be proportional to the width of the band, so to get a figure that depends on the source itself and not on our choice of band-width, we divide the power within the band by $$\Delta \lambda$$. This, or strictly $$\lim \limits_{\Delta \lambda\to 0} \frac{\Delta P}{\Delta \lambda}$$, gives the spectral power per unit area in units of $$\text W\ \text m^{-2}\ \text m^{-1}$$.