Explain the effect of potential difference on photoelectric current.

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Q. Explain the effect of potential difference on photoelectric current.

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Concept understanding — Stopping Potential

The stopping potential (also called the cut-off potential), denoted $V_0$ , is the specific negative (retarding) potential applied to the collecting electrode in a photoelectric-effect apparatus that is just sufficient to stop even the most energetic photoelectrons emitted from the cathode and reduce the photocurrent to exactly zero. As the retarding potential on the collecting electrode is made increasingly negative starting from zero, the photocurrent does not drop to zero immediately (since photoelectrons are emitted with a whole range of different kinetic energies, and the most energetic ones can still overcome a modest retarding field), but falls progressively as more and more electrons are turned back, reaching zero only once the retarding potential reaches the specific value $V_0$ at which even the fastest photoelectrons are brought to rest exactly at the collecting electrode.

At the stopping potential, the work done by the retarding field on the fastest photoelectron, $eV_0$ , exactly equals that electron's initial (maximum) kinetic energy, giving the defining relation $K_{max}=\tfrac12mv_{max}^2=eV_0$ . Measuring $V_0$ at a fixed, known frequency of incident light is therefore a direct, practical way of measuring $K_{max}$ experimentally. Repeating this measurement at several different intensities (holding frequency fixed) shows $V_0$ stays exactly constant, confirming that the stopping potential -- and hence $K_{max}$ -- is independent of light intensity. Repeating it instead at several different frequencies (holding intensity fixed) shows $V_0$ grows larger as frequency increases, and a graph of $V_0$ against frequency is a straight line that crosses zero exactly at the metal's threshold frequency $\nu_0$ -- the frequency below which no stopping potential (and no photocurrent at all) can be measured, since no photoelectrons are emitted in the first place.

Step 1. With the frequency and intensity of the incident light held fixed, the anode potential relative to the cathode is varied and the resulting photocurrent recorded.

Step 2. Starting from a positive anode potential and increasing it, the photocurrent rises steadily, then flattens out at a maximum, constant saturation current -- reached once every photoelectron emitted from the cathode is being collected at the anode, so increasing the potential further cannot raise the current any more.

Step 3. Applying a negative (retarding) potential to the anode instead does not drop the current to zero immediately, since photoelectrons are emitted with a range of different kinetic energies and the more energetic ones can still overcome a modest retarding field.

Step 4. As the retarding potential is made progressively more negative, more and more photoelectrons are turned back and the current steadily falls, reaching exactly zero at a specific negative potential $-V_0$ , the stopping potential -- the minimum retarding potential able to stop even the most energetic photoelectrons.

Step 5. At the stopping potential, the work done against the retarding field on the fastest electron exactly equals its initial kinetic energy: $K_{max}=\tfrac12mv_{max}^2=eV_0$ . Repeating this study at several fixed intensities shows the saturation current rising with intensity, but the stopping potential $V_0$ staying exactly constant.

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V_0

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Q.Explain the effect of potential difference on photoelectric current.

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