What is the number of photons of light with a wavelength of 4000 pm that provide 1J of energy?
Given:
Wavelength, λ = 4000 pm
Energy, E = 1 J
By Planck’s relation we have,
Energy, E = h×v
But we know v = [c] / [λ]
Where
c = Speed of Light
v= Frequency
λ = Wavelength
So, E = hc /λ
= [[6.626×10-34] × [3×108]] / [4000×10-12]
= [1.9878×10-25] / [4000×10-12]
= 4.9695×10-17 J
4.9695×10-17 J is the Energy of 1 photon
So, 1 J is the energy of X number of photons
X = [1] / [4.9695×10-17]
X = 2.012×1016 photons
So, the number of photons which provide 1 J of energy is 2.012×1016 photons.