Answer: The energy of a mole of photons is [tex]2.46\times 10^{5}J[/tex]
Explanation:
The relation between energy and wavelength of light is given by Planck's equation, which is:
[tex]E=\frac{N_Ahc}{\lambda}[/tex]
where,
E = energy
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
c = speed of light = 3.0\times 10^8m/s
[tex]N_A[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
[tex]\lambda[/tex] = wavelength of photon = 486 nm = [tex]486\times 10^{-9}m[/tex] (Conversion factor: [tex]1m=10^9nm[/tex] )
Putting values in above equation, we get:
[tex]E=\frac{6.022\times 10^{23}\times 6.626\times 10^{-34}Js\times 3.0\times 10^8m/s}{486\times 10^{-9}m}\\\\E=2.46\times 10^{5}J/mol[/tex]
Hence, the energy of a mole of photons is [tex]2.46\times 10^{5}J[/tex]
