# What is $n$ in $E=nhf$? Is it the number of photons or energy state of atom?

I've been searching for the answer all over the internet, and all I found is two different answers and I need to know what answer is right.

$$E=nhf$$ is an equation to find the 'total energy' for a group of photons in the same frequency; for a single photon $$E= hf$$, is often expressed as $$E= h\nu$$; $$n$$ being the total number of photons. Because photons tend to travel in large groups, be better using this one: $$E = n\cdot N_A \cdot h\cdot f$$ In this equation $$n$$ is the number of moles, and $$N_A$$ is Avogadros number.

The $$n$$ refers to the nth state of vibration, $$f$$ is the frequency of the lowest energy state, $$h$$ is a constant called the Planck constant, and $$E_n$$ is the energy of the $$n-$$th level of vibration.

So who's right?

• It depends if you want to know the energy of a group of photons, or of a single photon that's known to have a frequency that's a harmonic of some known fundamental. Oct 5, 2021 at 19:37
• and how is that related to the nth state of vibration(energy state of atom)? (please elaborate because i'm new to atomic physics) Oct 6, 2021 at 4:24
• My point is that that equation could be applied in either situation. Physics is more than just a pile of equations. You need to understand how each equation describes a physical situation...and it's entirely possible for one equation to apply to more than one situation (possibly with different defintions of the symbols used in the equation). Oct 6, 2021 at 4:46
• ah okay thanks a lotttt Oct 6, 2021 at 5:40

Photons are excitations of the electromagnetic field. Luckily, the energy levels of an EM wave with frequency $$f$$ are equally separated by an energy difference of $$hf$$, meaning that saying "this light wave has $$n$$ photons" is by definition meaning that the EM wave is in its $$n$$'s energy level (when the ground state is counted as $$0$$).