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Calculate the number of photons of light with a wavelength of 3000 pm that provide 2 J of energy.

Expert Answer

It is required to calculate the total number of photons having a total energy of 2 J. Energy of one photon can be calculated as,
Here, ‘h’ is Planck’s constant and ‘ν’ is the frequency of radiation. Expressing ν in terms of speed of light (c)  and wavelength (λ),
Substituting the value of ‘ν’ in equation, we get the energy of one photon, which is given as,
The equation obtained in the previous step is the energy of a single photons and for ‘N’ photons, the total energy is given as,
The total energy of ‘N’ photons is given as 2 J,
c = 3 x 108 m/s, h = 6.63 x 10-34 J-s and λ = 3000 pm
since, 1 pm = 10-12 m
therefore, λ = 3000 x 10-12 m

Substituting the values in the equation, we get,

The total number of photons having an energy of 2 J is 3.0 x 1016