What is the energy (in J) of 1 mole of the photon?

Question

A photon has a wavelength of 5.36  10−7 m. What is the energy (in J) of 1 mole of the photon? 

Answer 1

First we will find the frequency as follows:

c = λν

c = speed of light = 3x10⁸ m/sec

λ = wavelength = 5.36x10^-7 m

ν = frequency = ?

ν = c/λ = 3x10⁸ msec^-1 / 5.36x10^-7m = 5.60x10¹⁴sec^-1

Now we use this frequency to find the energy, as follows:

E = hν

E = energy

h = Planck's constant = 6.626x10^-34 J-sec

ν = frequency = 5.60x10¹⁴sec^-1

E = 6.626x10^-34 J-sec * 5.60x10¹⁴sec^-1 = 3.71x10^-19 Joules (this is the energy of ONE photon)

To get energy of 1 mole of photons, we multiply by Avogadro's number, 6.02x10²³ photons/mole

3.71x10^-19 J/photon x 6.02x10²³ photons/mole = 2.23x10⁵ J