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. 

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