I have an example class yesterday, but one question troubled me. In part (b), why does E=nhf? For me, it seems E=nh is enough, why does the equation involve frequency f after quantization?
One answer might be: The unit of E (energy) is a Joule, the unit of h (Plank's constant) is Joule time a second. If you want the equation to be correct you need to multiply h with something that has units of 1 over a second. Roman.
What do you mean "E = nh is enough"? That equation is not correct, because as pointed out above, the units are not correct.
h = energy per cycle. f = number of cycles per unit of time. your quantization must include a quantization of time.
Energy within a single system is quantized, but there are different energies that result from following the E=nh model in different systems, so if you consider every possible system energy is continuous, just like the light spectrum.