Q.The photoelectric work function for a metal surface is $3.84 \times 10^{-19}$ J. If the light of wavelength 5000 Å is incident on the surface of the metal, will there be photoelectric emission?

The work function of a metal, denoted $\phi_0$ and conventionally measured in electron-volts (eV), is defined as the minimum energy an electron must be given to escape from that metal's surface -- in other words, the height of the surface potential barrier that a free electron must overcome to be emitted. One electron-volt is itself defined as the kinetic energy an electron gains when accelerated through a potential difference of exactly 1 V: since work done equals charge times potential difference, $1\ \text{eV}=qV=(1.602\times10^{-19}\ \text{C})(1\ \text{V})=1.602\times10^{-19}\ \text{J}$, giving a convenient, human-sized unit of energy for atomic and nuclear-scale problems where the SI joule would otherwise involve unwieldy powers of ten. …