# What is the energy of one mole of photons?

## Answer #1

The **energy** \( W_{\text p} \) of a single photon is given by the following quantum hypothesis:

**Energy of a photon using wavelength**

Here \( c ~=~ 3 \cdot 10^8 \, \frac{\mathrm m}{\mathrm s} \) is the speed of light and \( h ~=~ 6.6 \,\cdot\, 10^{-34} \, \mathrm{Js} \) is the Planck's constant. The energy \(W_{\text p}\) of a photon depends only on the **wavelength** \( \lambda \) of the light.

The **energy of one mole of photons**, let us call it \(W_{\text{mol}}\), is the energy \(W_{\text p}\) of a single photon multiplied by the number of photons per mole. The **Avogadro constant** \(N_{\text A} = 6 \cdot 10^{23} \, \frac{1}{\mathrm{mol}} \) provides us with the number of photons per mole. Therefore, the photon energy per mole is given by:

**Photon energy per mole is the product of the Avogardo constant with the energy of a photon**

Substitute equation 1

into 2

:

**Photon energy per mole using wavelength**

So if you insert a concrete wavelength \(\lambda\) into Eq. 3

, you get the energy of \( 6 \cdot 10^{23} \) photons, which just form one mole.

You can express the energy \( W_{\text p} \) of a photon with the **light frequency** \(f\):

**Energy of a photon using frequency**

Thus, the photon energy per mole can also be calculated in the following way:

**Photon energy of one mole using frequency**