The wavelength of light would have to fall on sodium is 392.30 nm.
Given data:
The work function of sodium metal is, [tex]W_{0}=2.46 \;\rm eV=2.46 \times (1.6 \times 10^{-19})=3.936 \times 10^{-19}\;\rm J[/tex].
The maximum speed of electrons is, [tex]v=0.50 \times 10^{6} \;\rm m/s[/tex].
The energy of electrons due to its continuous motion is known as kinetic energy. The standard expression for the kinetic energy of electron is,
[tex]E = \dfrac{hc}{\lambda}-W_{0}[/tex]
here, [tex]\lambda[/tex] is the wavelength of light, h is the Planck's constant and c is the speed of light.
Solving as,
[tex]\dfrac{1}{2}mv^{2} = \dfrac{hc}{\lambda}-W_{0}\\\\\dfrac{1}{2} \times (9.1 \times 10^{-31}) \times (0.50 \times 10^{6})^{2} = \dfrac{ 6.63 \times 10^{-34} \times 3 \times 10^{8}}{\lambda}-3.936 \times 10^{-19}\\\\\lambda =3.92 \times 10^{-7} \;\rm m\\\\\lambda =(3.92 \times 10^{-7}) \times (10^{9})\\\\\lambda =392.30 \;\rm nm[/tex]
Thus, we can conclude that the wavelength of light would have to fall on sodium is 392.30 nm.
Learn more about the kinetic energy of electrons here:
https://brainly.com/question/13145345
