Focus 1 Exercises 1.31

[rita_h]

For this exercise, we have the wavelength of the GaN laser given( 405nm) and that of the red ruby laser given (694 nm). I know that we should find the energies of each using E = hc/lambda, and then we'd compare that to the given threshold energy (which we find to be 4.694 * 10^-19 J).
My question is, couldn't we have found the wavelength of the given threshold energy (which would turn out to be 423 nm), then compared it to the given wavelengths?
(It's close to 405 nm- and we'd reach the same conclusion [GaN is the required laser]).

[Nancy Li 1C]

Someone can correct me, but I believe both ways should be fine! Logically, the first way makes more sense since the threshold energy isn't part of a light being shone (and thus doesn't really have a wavelength) but mathematically, both ways work.