Experimental study of the photoelectric effect

What does the photoelectric experiment show?

In plain words: brighter light knocks out more electrons, but not faster ones. To stop even the fastest electrons you need a certain reverse voltage, and that voltage depends on the colour (frequency) of the light, not on its brightness. Below a certain frequency nothing comes out at all.

Regime: the standard one-photon photoelectric model at ordinary intensity, with a fixed clean surface and negligible heating, space charge, contact-potential offsets and background current. Multiphoton/strong-field emission can occur outside this regime. “Instantaneous” means no classical energy-accumulation delay, not literally zero interaction time or zero random waiting time for the next photon. Photon absorption does not guarantee electron escape. At fixed frequency, unchanged illuminated area and collection efficiency are needed for current to scale with intensity. V_₀ is a positive stopping-voltage magnitude; the ideal collector potential at cutoff is −V_₀ relative to the emitter.

The experimental set-up

• An evacuated glass or quartz tube, as in Lenard’s experiment, holds a thin photosensitive plate C and a metal plate A. Monochromatic light from a source S passes through a quartz window W, which lets ultraviolet light through, and falls on C (NCERT page 277, Figure 11.1).
• A battery keeps a potential difference between C and A that can be varied, and a commutator reverses it, so A can be made positive or negative with respect to C. A voltmeter measures the potential difference and a microammeter the photocurrent (NCERT page 277).
• The arrangement can study how the photocurrent depends on (a) the intensity of the light, (b) its frequency, (c) the potential difference between A and C, and (d) the material of C. Filters select a wavelength band from a broadband source rather than changing each photon’s frequency; moving the source changes the intensity (NCERT pages 277–278).
• When A is positive, the electrons from C are attracted to it and a current flows in the circuit (NCERT page 277). The current in the circuit is an ordinary electric current, carried across the tube by the photoelectrons.

Effect of intensity of light on photocurrent

• With A positive and the frequency and potential fixed, the photocurrent increases linearly with the intensity of the light (NCERT page 278, Figure 11.2).
• The photocurrent equals e times the number collected per second; if the collection fraction is fixed, it is proportional to the number emitted per second, so that number is proportional to the intensity (NCERT page 278).

Effect of potential on photoelectric current

• With the frequency and intensity fixed, making A more positive (an accelerating potential) increases the photocurrent at first (NCERT page 278).
• Making A negative (a retarding potential) repels the electrons, and only the more energetic ones reach A. The current falls rapidly and becomes zero at a sharply defined negative potential −V₀ (NCERT page 278, Figure 11.3).

Saturation current

• Beyond a certain positive potential of A, all the electrons emitted by C are collected and the current stops rising. This maximum current is the saturation current (NCERT page 278).
• For one frequency, the saturation current is proportional to the intensity: more intense light releases more electrons per second (NCERT page 279, Figure 11.3).
• For the comparison of frequencies, NCERT says it sets “the same intensity of light radiation at various frequencies” and gets the same saturation current (NCERT page 279, Figure 11.4). Take this with care: a photon of higher frequency carries more energy, so light of equal intensity brings fewer photons each second and would not, in general, give the same current. Read Figure 11.4 as light adjusted to release the same number of electrons per second (reasoned from NCERT pages 282–283).

Stopping potential

• The stopping (or cut-off) potential V₀ is the least retarding potential of A at which the photocurrent becomes zero (NCERT page 278).
• The emitted electrons do not all have the same energy. The current stops when the retarding potential turns back even the most energetic ones, those with the maximum kinetic energy K_max (NCERT Eq. (11.1), page 279):

• For a given frequency the stopping potential is the same for every intensity (NCERT page 279, Figure 11.3). So K_max depends on the light source and the emitter material, but not on the intensity (NCERT page 279).

Effect of frequency of incident radiation on stopping potential

• With the light at each frequency adjusted to give the same saturation current, the stopping potential changes: it is larger in size for higher frequencies, V₀₃ > V₀₂ > V₀₁ for ν₃ > ν₂ > ν₁. So the higher the frequency, the greater the maximum kinetic energy of the photoelectrons (NCERT page 279, Figure 11.4).
• A graph of stopping potential against frequency is a straight line for each photosensitive material (NCERT page 279, Figure 11.5).
• The lines for different metals are parallel. NCERT explains why in Section 11.6: NCERT Eq. (11.4) gives every line the same slope h/e, whatever the metal (NCERT pages 282–283).
• NCERT slip (page 279): the caption of NCERT Figure 11.5 speaks of “a given photosensitive material”, but the graph shows two metals, one line for each.

Threshold frequency

• Each line meets the frequency axis at a minimum cut-off frequency ν₀, where the stopping potential is zero. Below ν₀ no photoelectric emission is possible, however intense the light. This threshold frequency is different for different metals (NCERT pages 279–280).
• Different materials respond differently: selenium is more sensitive than zinc or copper, and ultraviolet light ejects electrons from copper while green or red light does not (NCERT page 280).
• Above the threshold, emission starts instantaneously, with no apparent time lag even for very dim light: within about 10⁻⁹ s or less (NCERT page 280).
• The four observations (NCERT page 280): (i) photocurrent ∝ intensity; (ii) saturation current ∝ intensity, stopping potential independent of intensity; (iii) a threshold frequency below which there is no emission, and above it the stopping potential, and so K_max, rises linearly with frequency; (iv) emission is instantaneous.

Solved examples

Common mistakes to avoid

Quick revision summary

• Set-up: emitter C, collector A, quartz window, variable and reversible potential, microammeter.
• Photocurrent and saturation current are proportional to the intensity.
• Stopping potential V₀: the retarding potential at which the current stops; K_max = eV₀, independent of intensity.
• Higher frequency gives a larger stopping potential; V₀ against ν is a straight line for each metal.
• Below the threshold frequency ν₀ there is no emission at all; above it emission is instantaneous (about 10⁻⁹ s).

Questions students ask

Why is the stopping potential negative, and how is it different from a retarding potential?

The stopping potential is negative because it is the collector’s potential relative to the emitter, and the collector must be negative to push the photoelectrons back; V₀ is quoted as its size, so that K_max = eV₀ is positive (NCERT pages 278–279). Any negative collector potential is a retarding potential: a small one turns back only the slower electrons, so the current falls but does not stop. The stopping potential is the least retarding potential that turns back even the fastest, making the current zero; on the current–potential graph it is where each curve meets the axis, at −V₀.

Why does the stopping potential not depend on the intensity of light?

The stopping potential does not depend on the intensity because it measures only the largest kinetic energy one electron carries away, and each electron gets its energy from a single quantum of light, hν, set by the frequency alone (NCERT pages 279 and 281–282). Brighter light of the same frequency brings more quanta each second, so more electrons and a larger current, but no electron gets more energy: in Einstein’s equation, eV₀ = hν − φ₀, only the frequency and the metal appear. The wave picture expected the opposite.

Why does a photocurrent flow even when the collector is at zero potential?

A photocurrent flows at zero collector potential because the photoelectrons leave the emitter with kinetic energies of their own, from almost zero up to K_max, so many reach the collector unaided: the light, not the battery, drives the current (reasoned from NCERT Figure 11.3, page 278). A positive potential also gathers those that would miss the collector or fall back, until all arrive at saturation; a negative one turns back first the slowest and then faster ones, so the current falls rapidly but not in one step, reaching zero at −V₀. The energies are spread because the metal’s free electrons start with different energies (NCERT Points to ponder 2–3, page 288).

Does the saturation current depend on the frequency of the light?

For fixed frequency and quantum yield, saturation current is proportional to intensity. Frequency independence is not a general law: NCERT says the photocurrent depends on the intensity, the potential difference and the emitter material (Summary point 3, page 287), and its Figure 11.4 shows one saturation current at three frequencies (page 279). At equal intensity, though, higher-frequency light brings fewer photons, each carrying more energy hν. For a metal from which both can eject electrons, 340 nm light brings only 2/3 as many photons as 510 nm light, so if each photon were as likely to free an electron, its saturation current would be 2/3 as large (reasoned from NCERT pages 282–283).

What does the graph of stopping potential against wavelength look like?

Against wavelength, the stopping potential falls along a curve, not a straight line, because V₀ = hc/(eλ) − φ₀/e: it is large at short wavelengths and falls to zero at the threshold wavelength, beyond which there is no emission (reasoned from NCERT Eq. (11.4), page 282, and c = νλ). Plotted against 1/λ instead, it is a straight line whose slope, hc/e ≈ 1.24 × 10^⁻⁶ V m, is the same for every metal, like the graph against frequency.

What are the SI unit and dimensional formula of stopping potential?

The stopping potential is a potential difference, so its SI unit is the volt and its dimensional formula is [M L^² T^⁻³ A^⁻¹] (NCERT page 288), as for any electric potential. That follows from potential being energy per unit charge: [M L^² T^⁻²] divided by the dimensions of charge, [A T].

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. What is the saturation current in a photoelectric experiment?

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   The largest photocurrent, reached when the collector is positive enough to collect every electron the emitter releases (NCERT page 278).

2. Q2. The stopping potential is 2.0 V. Find the maximum kinetic energy of the photoelectrons in eV and in joules.

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   K_max = eV₀ = 2.0 eV = 3.2 × 10⁻¹⁹ J (NCERT Eq. (11.1), page 279).

3. Q3. Which of these changes the stopping potential: (a) the intensity of the light, (b) its frequency, (c) the metal of the emitter?

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   (b) and (c). The stopping potential is independent of the intensity (NCERT pages 279 and 287, Summary point 4).