The work function of a metal is 31 eV. To eject a photoelectron of zero velocity from the surface of the metal the wavelength of incident light should be above

The work function of a metal is the minimum energy required to remove an electron from the surface of the metal. This energy is given in electron volts (eV).

The energy of a photon (light particle) is given by the equation E = hc/λ, where h is Planck's constant (4.136 x 10^-15 eV.s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light.

To eject a photoelectron with zero velocity, the energy of the photon must be equal to the work function of the metal. Therefore, we can set up the equation:

31 eV = (4.136 x 10^-15 eV.s)(3 x 10^8 m/s) / λ

Solving for λ gives us:

λ = (4.136 x 10^-15 eV.s)(3 x 10^8 m/s) / 31 eV

This simplifies to:

λ = 4.01 x 10^-7 m, or 401 nm.

Therefore, the wavelength of incident light should be above 401 nm to eject a photoelectron of zero velocity from the surface of the metal.