Answer:
[tex]7.53\cdot 10^{20}[/tex]
Explanation:
The energy of a photon of wavelength [tex]\lambda[/tex] is given by
[tex]E=\frac{hc}{\lambda}[/tex]
where
[tex]h = 6.63\cdot 10^{-34} Js[/tex] is the Planck constant
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light
In this problem, the wavelength of the photon is
[tex]\lambda=600 nm=600\cdot 10^{-9} m[/tex]
So the energy of one photon with this wavelength is
[tex]E_1=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{600\cdot 10^{-9} m}=3.32\cdot 10^{-19} J[/tex]
In order to have a total energy of E = 250 J in this radiation, we have to divide this value by the energy of a single photon, so we find the number of photons that we need:
[tex]n=\frac{E}{E_1}=\frac{250 J}{3.32\cdot 10^{-19} J}=7.53\cdot 10^{20}[/tex]
