We must use two formulas of energy first how energy is related to wavelength:
[tex]E=\frac{hc}{\lambda}[/tex]
Such that [tex]\lambda=Wavelength[/tex], c is the speed of light in a vacuum and h is Plank's constant.
And the second equation is how energy relates to voltage:
[tex]E=qV[/tex]
Such that q is the charge of the particle (in this case the electron) and V is voltage. By substituting the second equation into the first we have:
[tex]E=\frac{hc}{\lambda}\\ \\qV=\frac{hc}{\lambda} \\\\V=\frac{hc}{\lambda q}[/tex]
We know that:
[tex]c=2.99 \times 10^8 m/s\\\\q=e=1.6 \times 10^{-19} C\\\\h= 6.67 \times 10^{-34} m^2kg/s\\\\\lambda=0.57 \times 10^{-9}m[/tex]
And so:
[tex]V=\frac{hc}{\lambda q}=\frac{(6.67 \times 10^{-34})(2.99 \times 10^8)}{(0.57 \times 10^{-9}) (1.60 \times 10^{-19})}[/tex]
[tex]V=2186.77 Volts[/tex]
