Question

What is the energy in joules of a mole of photons associated with visible light of wavelength 486 nm?

Answer 1

Answer:

$2.46\cdot 10^5 J$

Explanation:

The enegy of a single photon is given by:

$E=\frac{hc}{\lambda}$

where

h is the Planck costant

c is the speed of light

$\lambda$ is the wavelength of the photon

In this problem,

$\lambda=486 nm=4.86\cdot 10^{-7}m$

so the energy of one photon is

$E_1=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{4.86\cdot 10^{-7}m}=4.09\cdot 10^{-19} J$

1 mole of photons contains a number of Avogadro of photons:

$N_A = 6.022\cdot 10^{23}$

therefore, the total energy of 1 mole of these photons will be

$E=N_A E_1 = (6.022\cdot 10^{23})(4.09\cdot 10^{-19} J)=2.46\cdot 10^5 J$