# What does 'per unit frequency' refer to?

We were discussing Kirchoff's theorem on blackbody radiation in class today and the equation was: $$e_{f}= J(f,T)$$

$$e_f$$ was defined as power per unit area per unit frequency. What does per unit frequency refer to here? I know what per unit time means but don't understand 'per unit frequency'.

The blackbody radiation is radiation with not only one frequency (e.g. like in a laser beam). Instead it is a mixture of many frequencies (essentially all frequencies from $$0$$ to $$\infty$$).
Therefore it doesn't make much sense to ask for the radiation power at a single frequency $$f$$. But it makes perfect sense to ask for the radiation power in a frequency range (from $$f_1$$ to $$f_2$$).
Power per unit area and per unit frequency just means the power emitted from an area of $$1$$ m$$^2$$ in a frequency range of $$1$$ Hz (for example in the range from $$500$$ THz to $$500.000000000001$$ THz).
The spectrum below shows the radiation power per area (measured in m$$^2$$) and per frequency range (measured in Hz) as it varies depending on the frequency (here given in THz).
To begin with, power per unit area gives the intensity. So, basically, $$e_f$$ is denoting the Intensity per unit frequency. It can give an idea about intensity of radiation absorbed by the black body for a range of frequency.