Higher Work Function and Electron Velocity?

[KC Navarro_1H]

For the photoelectric effect, what is the relationship between joules and ejected electron velocity? A quiz question that relates to this is:

"The work function of silver is 6.83 x . 10^-19 J per atom. The work function of gold is 8.17 x 10^-19 J per atom. If the same light source shines on both metals and causes electrons to be ejected from both, which metal will faster electrons be ejected?"

The correct answer is silver, but I don't really understand why? Thank you in advance!

[Beverly Shih 1K]

The work function is how much energy it takes to remove an electron from a metal, and the velocity of the removed electron depends on how much energy is left after being removed. The equation that relates these two concepts is: Energy of photon - work function = kinetic energy of electron, and kinetic energy of electron = 1/2 mv^2 . So in the question, silver has a lower work function so there is more energy left over that becomes kinetic energy of the electron. Because the electron has higher kinetic energy, it has a higher velocity as well.