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Question

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

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,
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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),
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Substituting the value of ‘ν’ in equation, we get the energy of one photon, which is given as,
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The equation obtained in the previous step is the energy of a single photons and for ‘N’ photons, the total energy is given as,
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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,

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