Experimental Study of the Photoelectric Effect

The Photocell Apparatus

The experimental study uses an evacuated glass or quartz tube containing two electrodes: a thin photosensitive plate C, the emitter, and a metal plate A, the collector. Monochromatic light of sufficiently short wavelength from a source S passes through a window W and falls on plate C. A transparent quartz window is used because it transmits ultraviolet radiation, which many photosensitive metals require.

A battery maintains a variable potential difference between C and A, and a commutator can reverse the polarity, so that A may be held at any desired positive or negative potential with respect to C. A voltmeter (V) reads the potential difference; a microammeter (mA) reads the resulting photocurrent. Three quantities can be varied independently — the intensity of light, the frequency of light, and the collector potential — and the nature of the emitter material can also be changed. The microammeter is appropriate because the currents are tiny: NIOS §25.3 notes that the saturation current in such a phototube is typically of the order of nanoamperes.

Several design choices in the apparatus matter for reading the results correctly. The tube is evacuated so that emitted electrons travel from C to A without colliding with gas molecules; in NIOS §25.1.1 the same arrangement is described with C as a metallic photo-cathode and A as the collecting plate. The quartz window is essential because ordinary glass absorbs ultraviolet, and many emitters such as zinc respond only to ultraviolet light. The commutator lets the experimenter switch A between accelerating (positive) and retarding (negative) potentials without rewiring, which is what makes the full current–potential curve accessible in one sitting. Light of a chosen frequency is selected by a coloured filter or coloured glass placed in the beam, while intensity is set by the source-to-emitter distance — moving the source closer raises the intensity in proportion to the inverse square of the distance.

The strategy of the whole study is to vary one of these quantities while holding the others fixed, and watch a single measured response. With this single instrument NCERT §11.4 carries out three distinct experiments: the dependence of photocurrent on intensity, on collector potential, and on frequency. Each isolates a different aspect of the emission, and together they fix the laws that the photoelectric effect obeys.

Effect of Intensity on Photocurrent

To isolate the role of intensity, the collector A is kept at a fixed positive potential and the frequency is held constant, so that every emitted electron is collected. Only the intensity of the incident light is varied — in practice by changing the distance of the source from the emitter — and the photocurrent is recorded each time.

The result is a straight line through the origin: the photocurrent increases linearly with intensity. Because the photocurrent is proportional to the number of photoelectrons released per second, this shows that the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.

It is worth being precise about what intensity controls and what it leaves untouched. Intensity governs the population of emitted electrons, not the energy of any individual electron. NIOS §25.1.1 records the same result by counting photoelectrons released per unit area of the emitting surface, which again varies linearly with intensity. Keeping the collector at a fixed positive potential during this run is what guarantees that the measured current is the genuine emission rate: at that potential essentially every electron leaving C is collected, so the microammeter is reading the supply of photoelectrons rather than how efficiently they are being swept across.

Effect of Collector Potential

Next the frequency and intensity are fixed and the collector potential is swept. With A made gradually more positive, the photocurrent rises as more electrons are drawn across, until at a sufficiently high accelerating potential every emitted electron reaches A. Beyond this point the current cannot grow; it levels off at the saturation current, which corresponds to all photoelectrons from C arriving at A.

The polarity is then reversed and A is made increasingly negative. Now only the more energetic electrons can climb the retarding potential, so the current falls rapidly to zero at a sharp critical value $V_0$, the stopping potential (or cut-off potential). At $V_0$ even the fastest photoelectron is turned back, so the stopping potential measures the maximum kinetic energy of the photoelectrons:

$$ K_{\max} = e\,V_0 $$

The reason the cut-off is sharp and well defined is that the photoelectrons leave the emitter with a spread of kinetic energies, from nearly zero up to $K_{\max}$. As the retarding potential is increased, the slower electrons are turned back first and the current falls gradually; it reaches zero only when the potential is large enough to repel even the fastest electron in the distribution. That fastest electron carries the maximum kinetic energy, so the stopping potential is a direct, single-number readout of $K_{\max}$ for the chosen frequency and metal — independent of how the slower electrons are distributed.

Repeating the sweep at higher intensities $I_2$ and $I_3$ (with $I_3 > I_2 > I_1$, same frequency) raises the saturation current each time, confirming that more electrons are emitted per second. The stopping potential, however, does not change — all the curves cut the potential axis at the same $V_0$. For a given frequency, the stopping potential is independent of intensity, so $K_{\max}$ depends on the light source and the emitter metal but not on how bright the light is.

Effect of Frequency on Stopping Potential

In the third experiment the intensity is held the same while the frequency of incident light is changed using coloured filters, and the current–potential curve is recorded for each frequency. The saturation currents come out equal (same intensity), but the stopping potentials differ: higher frequency gives a more negative stopping potential. With frequencies ordered $\nu_3 > \nu_2 > \nu_1$, the stopping potentials follow $V_{03} > V_{02} > V_{01}$.

This means greater frequency produces photoelectrons of greater maximum kinetic energy, so a larger retarding potential is needed to stop them. Plotting $V_0$ against $\nu$ for a given metal yields a straight line. The line shows two facts: $V_0$ varies linearly with frequency, and there is a minimum cut-off frequency $\nu_0$ at which $V_0$ is zero. Below $\nu_0$ no emission occurs however intense the light, so $\nu_0$ is the threshold frequency — characteristic of the metal and different for different metals.

The logic of the third experiment is the mirror image of the second. In the potential experiment the frequency was frozen and intensity was the variable, which let the saturation current move while $V_0$ stayed pinned. Here the intensity is frozen and frequency is the variable, which pins the saturation current — all curves saturate together — while $V_0$ moves. Holding one of intensity or frequency constant at a time is precisely what lets the experiment separate the two distinct responses, the count of electrons and the energy of each electron, that a single combined run would blur together.

The threshold is a property of the emitter, not of the light. NCERT §11.4.3 notes that different photosensitive materials respond differently: selenium is more sensitive than zinc or copper, and the same material reacts differently to different wavelengths. Ultraviolet light produces photoelectric emission in copper, whereas green or red light does not. The metals zinc, cadmium and magnesium respond only to short-wavelength ultraviolet, while alkali metals such as lithium, sodium, potassium, caesium and rubidium are sensitive even to visible light — they have lower threshold frequencies. This is exactly why the $V_0$–$\nu$ lines for two metals in Figure 4 are parallel but cut the frequency axis at different points: the slope is common, but each metal carries its own $\nu_0$.

What the Data Fix and What They Free

Across the three experiments, four observations stand out. They are worth holding as a single table because NEET questions almost always test the contrast between intensity-controlled and frequency-controlled quantities.

A fifth feature is timing. Provided the frequency is above threshold, emission begins essentially instantaneously — within about $10^{-9}$ second or less — even for very dim light. There is no measurable lag while energy accumulates, in contrast to what continuous-wave absorption would predict. Taken together, these five observations — linear dependence of current on intensity, intensity-controlled saturation current, frequency-controlled stopping potential, the existence of a metal-specific threshold, and instantaneous emission — are the complete experimental signature that the next subtopic must explain. The first attempt, the wave theory of light, fails on three of them at once: it predicts that $K_{\max}$ should grow with intensity, that no threshold frequency should exist, and that dim light should emit only after a long delay. The experimental study therefore does more than catalogue facts; it sets the precise bar that any successful theory of light has to clear.