Explanation:
It is known that relation between frequency and wavelength is as follows.
f = [tex]\frac{c}{\lambda}[/tex]
where, c = speed of light
[tex]\lambda[/tex] = wavelength
Hence, first we will calculate the frequency as follows.
f = [tex]\frac{c}{\lambda}[/tex]
= [tex]\frac{3 \times 10^{8} m/s}{6.61 m}[/tex]
= [tex]0.453 \times 10^{8}[/tex] s
Now, the relation between energy and frequency is as follows.
E = hf
where, h = planck's constant = [tex]6.63 \times 10^{-34}[/tex] J/s
E = [tex]6.63 \times 10^{-34} J \times 0.453 \times 10^{8}[/tex]
= [tex]3.00 \times 10^{-26} J[/tex]
or, = [tex]3.00 \times 10^{-29} kJ[/tex]
As one mole contains [tex]6.022 \times 10^{23}[/tex] atoms in a substance.
Hence, there are [tex]3.00 \times 10^{-29} kJ \times 6.022 \times 10^{23}[/tex]
= [tex]18.066 \times 10^{-6}[/tex] kJ/mol
Thus, we can conclude that radiation with wavelength of 6.61 m emits [tex]18.066 \times 10^{-6}[/tex] kJ/mol of energy.
