How many photons of light having a wavelength 400 nano meter are necessary to provide 1 joule of energy?
Here we will use the relation
E = hν (1)
where E is the energy of the photon, h is the planck's constant and ν is the frequency of the photon. Now we also have the relation
c = νλ
where c is the speed of light, ν is the frequency and λ is the wavelength. Therefore, equation (1) becomes
E = hc / λ
Thus the energy of 1 photon in a radiation of wavelength 400 nm is
= (6.63 X 10-34 X 3 X 108) / (4 X 10-7)
= 4.972 X 10-19 J
Now the number of photons that would be required to provide an energy of 1 joule
= ( 1 / 4.972 X 10-19)
= 2.011 X 1018
Therefore 2.011 X 1018 of photons would be required to provide 1 Joule of energy.