Question 14: A beam of red light and a beam of blue light have exactly the same energy. Which light contains the greater number of photons?

Physically, energy is directly proportional to the frequency of radiation or inversely proportional to the wavelength of the radiation. Now the frequency of blue light is greater than the frequency of red light  or wavelength of wavelength of blue light is smaller than the wavelength of red light. Therefore, if the number of photons of blue and red light is equal, the energy of the blue light would be more than the energy of red light. If energy of both radiations is the same, the number of photons of red light must be greater than the number of photons of blue light. Mathematically,

E = nhf (n is the number of photons).

(Because E/hc is constant)

Therefore, for larger wavelengths, number of photons must be greater. Red light has larger wavelength than the blue light, therefore, for equal energies the number of photons of red light must be greater than the number of photons of blue light.