# Formulae for energy of photon (E=hf and E=hv)

I have seen the energy of a photon given by the formulas:

$$E = h \cdot f \tag{1}$$ Where $E$ = energy of the photon, $h$ = Planck's constant, $f$ = frequency of radiation (Source: BBC article)

I've also seen it given as

$$E= h \cdot \nu \tag{2}$$ Where $\nu$ stands for frequency (Source: Wikipedia article)

But in this topic I've also seen

$$f=\nu/\lambda \tag{3}$$ Where $\nu$ = speed, $\lambda$ = wavelength (Source: Simple English Wikipedia article)

Is there any difference between equation 1 and equation 2? And is equation 3 unrelated?

• If you're talking photon energy with the Planck equation, you should be using $c$ for speed. – Zhe Nov 7 '16 at 21:21

I understand your confusion. They all are actually the same formulas. It is because lets start with the first equation,

$$E=h \cdot f$$

But we know that frequency can be written in terms of speed formula, $$v = f \cdot \lambda$$

Which can be rearranged into the following, $$\frac{v}{\lambda} = f$$

If you put that expression into the above equation, then that becomes

$$E = f \cdot \frac{v}{\lambda}$$

Hence the same formula can be written in many ways.

Your first two equations are just the same. $f$ usually stands for frequency and in the second equation you have just used $\nu$ for it. That is the frequency of the photon that is coming in or being released.

Whereas your third equation actually comes from the speed formula as I have written above, $$v = f \cdot \lambda$$

Rearranging for frequency, you get: $$\frac{v}{\lambda} = f$$

• Thanks for the answer @MathCurious314 :) So is it just a matter of v standing for different things in E=Hf and v=f*lambda? And the first two formulas are exactly the same? – K-Feldspar Nov 7 '16 at 20:35
• There is much extra in this answer, but fundamentally, author correctly points out that it is the same equation. Take heed orthoCresol's comment in question – Lighthart Nov 7 '16 at 20:57
• @K-Feldspar exactly. $v$ is being used for frequency in the second while it is being used for velocity in the third. :) – MathCurious314 Nov 7 '16 at 21:09