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.

1st answer

$E=nhf$ 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.

2nd answer

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?

  • 2
    $\begingroup$ 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. $\endgroup$
    – The Photon
    Oct 5, 2021 at 19:37
  • $\begingroup$ and how is that related to the nth state of vibration(energy state of atom)? (please elaborate because i'm new to atomic physics) $\endgroup$ Oct 6, 2021 at 4:24
  • $\begingroup$ 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). $\endgroup$
    – The Photon
    Oct 6, 2021 at 4:46
  • $\begingroup$ ah okay thanks a lotttt $\endgroup$ Oct 6, 2021 at 5:40

1 Answer 1


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 $0$).

  • $\begingroup$ so it's not the energy state of atom? $\endgroup$ Oct 5, 2021 at 20:13
  • $\begingroup$ @ElieMakdissi , nope. In the classical world, a small negative charge will orbit a big positive charge and that system has energy. Likewise, an electromagnetic wave also in the classical world has energy. When going to quantum mechanics, you see that the energy of the first system is quantized and has specific energy levels. This is true also for electromagnetic waves, and each excitation in the energy of an EM wave is called a photon. (So photons are not really particles in that "classic" manner, but excitations in energy of a wave. Nevertheless, today we understand all particles in such way) $\endgroup$ Oct 5, 2021 at 20:33
  • $\begingroup$ okay thanks a lot $\endgroup$ Oct 6, 2021 at 3:21

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