Question

Photoemission of electrons occurs from a metal \((\phi_0=1.96\,\text{eV})\) when light of frequency \(6.4\times10^{14}\,\text{Hz}\) is incident on it. Calculate the stopping potential.

Hint:

Remember: \[ eV_0=K_{\max}. \] Therefore, if \(K_{\max}\) is given in eV, the stopping potential is numerically equal to that value in volts.

Answer 1

Concept: The stopping potential is the minimum retarding potential required to stop even the fastest emitted photoelectrons from reaching the collector. The relation between stopping potential and maximum kinetic energy is \[ eV_0=K_{\max}. \] When kinetic energy is expressed in electron volts, the numerical value of stopping potential in volts is equal to the numerical value of kinetic energy in eV.

Step 1: Use the result obtained in part (b). Maximum kinetic energy of photoelectrons: \[ K_{\max}=0.69\,\text{eV}. \]

Step 2: Apply the stopping potential relation. \[ eV_0=K_{\max}. \] Since \(K_{\max}\) is already in electron volts, \[ V_0=0.69\,\text{V}. \]

Step 3: Interpret the result physically. A retarding potential of \(0.69\) volt is sufficient to stop the most energetic photoelectrons emitted from the metal surface. At this potential, the photoelectric current becomes zero. Final Answer: \[ \boxed{ V_0=0.69\,\text{V} } \]