Answer: The energy of a photon with a wavelength of 820 nm is [tex]2.42 \times 10^{-19} m[/tex].
Explanation:
Given : Wavelength = 820 nm
Convert nm into meter as follows.
[tex]1 nm = 10^{-9}\\So, 820 nm = 820 nm \times \frac{10^{-9} nm}{1 nm}\\= 820 \times 10^{-9} m[/tex]
The relation between energy and wavelength is as follows.
[tex]E = \frac{hc}{\lambda}[/tex]
where,
E = energy
h = Planck's constant = [tex]6.63 \times 10^{-34} kg m^{2}/s[/tex]
c = speed of light = [tex]3.0 \times 10^{8} m/s[/tex]
[tex]\lambda[/tex] = wavelength
Substitute the values into above formula as follows.
[tex]E = \frac{hc}{\lambda}\\= \frac{6.63 \times 10^{-34} kg m^{2}/s \times 3.0 \times 10^{8} m/s}{820 \times 10^{-9} m}\\= \frac{1.989 \times 10^{-25}}{820 \times 10^{-9}}\\= 2.42 \times 10^{-19} m[/tex]
Thus, we can conclude that energy of a photon with a wavelength of 820 nm is [tex]2.42 \times 10^{-19} m[/tex].
