Q:

What is the correct relationship between light intensity and wavelength?

So we looked at the emission line spectra of noble gases in the lab today (hydrogen, neon, helium). And I noticed that the brightest spectral line in the helium spectrum is the yellow one and the faintest was the violet/blue. But isn't wavelength related to energy by $E = \frac{hc}{λ}$? Since the yellow light has greater wavelength than the violet one, its energy should be lower and therefore shouldn't it be less intense? Or is there another relationship between intensity and wavelength? 

A:

The formula you cite gives wavelength related to the energy of an individual photon. The perceived brightness of a light source also depends on the number of photons which are present. The lower energy levels were brighter because they were being excited more frequently, because it's easier to drive an atom to less excited states. This means that more yellow photons were being emitted than others. (Addendum: I just also remembered that there could be some influence of human eye sensitivity here, but I don't know whether violet line in the series is far enough out that our eyes start to have trouble detecting it...)

