Explanation:
It is known that relation between energy and wavelength is as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
where, h = plank's constant = [tex]6.626 \times 10^{-34}[/tex]
c = speed of light = [tex]3 \times 10^{8} m/s^{2}[/tex]
[tex]\lambda[/tex] = wavelength
Convert nm into m as follows.
[tex]527 nm \times \frac{1 \times 10^{-9} m}{1 nm}[/tex]
= [tex]527 \times 10^{-9}[/tex] m
Therefore, calculate the energy as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
= [tex]\frac{6.626 \times 10^{-34} \times 3 \times 10^{8} m/s^{2}}{527 \times 10^{-9}}[/tex]
= [tex]0.037719 \times 10^{-17}[/tex] J
Hence, energy of the yellow light is [tex]0.037719 \times 10^{-17}[/tex] J.
Now, calculate the moles of yellow light as follows.
[tex]0.037719 \times 10^{-17} \times 6.022 \times 10^{23}[/tex]
= [tex]0.227144 \times 10^{6}[/tex] J
= 227144 J
or, = 227.14 kJ (as 1 kJ = 1000 J)
Thus, we can conclude that a mole of yellow photons of wavelength 527 nm has 227.14 kJ of energy.
