Question

Calculate the energy of one mole of photons of red light ($\mathbf{\lambda }=\mathbf{700}$ nm).

Short answer

The energy of one mole of photons of red light is$1.71\times {10}^5{\mathrm{Jmol}}^{-1}$.

Step-by-step solution

Definition of photon

The photon is a sort of fundamental particle that acts as the quantum of the electromagnetic field, which includes electromagnetic radiation such as light and radio waves and the electromagnetic force's force carrier.

Determine the energy.

The energy of a single photon can be calculated by using the equation below, where$\mathrm{c}$represents the speed of light,$\mathrm{h}$ represents Planck's constant, and$\mathrm{\lambda }$represents its wavelength.

$\begin{array}{c}\mathrm{E}=\frac{\mathrm{ch}}{\mathrm{\lambda }}\\ =\frac{(3\times {10}^8{\text{ms}}^{-1})(6.63\times {10}^{-34}{\text{m}}^2{\text{kgs}}^{-1})}{7\times {10}^{-7}\text{m}}\\ =2.84\times {10}^{-19}\text{J}\end{array}$

The energy of one mole of photons is calculated by multiplying the earlier supplied value of the energy of one photon by Avogadro's number.

$\begin{array}{c}{\mathrm{E}}_{1\mathrm{mol}}=(2.84\times {10}^{-19}\text{J})(6.02\times {10}^{23}{\text{mol}}^{-1})\\ =1.71\times {10}^5{\text{Jmol}}^{-1}\end{array}$