Stopping potential

Also called Stopping voltage

Stopping potential is the reverse potential difference that just halts the fastest photoelectrons, so no current flows. Multiplied by the elementary charge it gives the maximum kinetic energy of the ejected electrons.

The apparatus is set out at 15.5.A.3.iii: two metal plates in a vacuum chamber wired to a variable source of potential difference, one plate lit by monochromatic light, and the potential difference adjusted until no current is measured in the circuit. That reading is the stopping potential.

At that setting even the fastest photoelectron spends all of its kinetic energy crossing the potential difference, so

eVstop=Kmax⁡e V_{\text{stop}} = K_{\max}

This relation is not printed in the Modern Physics group of the sheet. It comes from ΔUE=qΔV\Delta U_E = q \Delta V in the Electricity group with q=e=1.60×10−19q = e = 1.60 \times 10^{-19} C, so cite that as the starting point rather than the result.

Substituting the photoelectric equation gives Vstop=(hf−ϕ)/eV_{\text{stop}} = (hf - \phi)/e, and two consequences carry most questions.

  • Stopping potential does not depend on intensity. A brighter beam of the same color raises the current and leaves the voltage that kills it unchanged.
  • A graph of VstopV_{\text{stop}} against frequency is a straight line of gradient h/eh/e, crossing the frequency axis at the threshold frequency.

Read the stopping potential in volts and Kmax⁡K_{\max} comes out directly in electron volts, since one electron moved through one volt is one electron volt.

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