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Physics · Ch 11 — Dual Nature of Radiation and Matter

Experimental Study of the Photoelectric Effect

11.4

Experimental Study of the Photoelectric Effect

The apparatus. The standard arrangement used to study the photoelectric effect quantitatively is described in this section's first figure: an evacuated tube containing an emitter plate C, on which the light to be studied is made to fall through a quartz window, and a separate collector plate A, connected through a sensitive microammeter and a battery-and-potentiometer arrangement that lets the potential difference between A and C be set to any chosen value, of either polarity. When light of a suitable frequency falls on C, photoelectrons are ejected from its surface; those that reach A are recorded as a photoelectric current on the microammeter.

Effect of intensity, at fixed frequency and fixed (positive) accelerating voltage. Keeping the frequency of the light fixed (above the threshold value for the metal used) and keeping plate A at a fixed positive potential relative to C (so that every emitted electron is pulled across to A), the photoelectric current is found to rise in direct, linear proportion to the intensity of the incident light -- doubling the intensity exactly doubles the current, confirming that intensity controls the NUMBER of photoelectrons emitted per second, and nothing else.

Effect of the applied (collector) potential, at fixed frequency and fixed intensity. Starting from a large positive potential on A (where every emitted electron reaches A, giving a current called the saturation current) and gradually reducing the potential, the current at first stays unchanged at its saturation value, then begins to fall as the potential is made negative -- because only the FASTER-moving electrons now have enough kinetic energy to fight against the retarding (opposing) electric field and still reach A. The current falls to exactly zero at one particular negative potential, called the stopping potential V0V_0 for that frequency and metal: at this potential, even the fastest photoelectrons emitted (those with the maximum kinetic energy KmaxK_{max}) are just barely turned back before reaching A. This gives a direct, purely electrical way to measure KmaxK_{max}, since the work the retarding field does on the fastest electron, eV0eV_0, must exactly equal that electron's kinetic energy:

Kmax=eV0K_{max} = eV_0

Repeating this at a HIGHER intensity but the SAME frequency gives a LARGER saturation current (more electrons per second) but the SAME stopping potential V0V_0 -- direct proof that KmaxK_{max} does not depend on intensity, exactly as Lenard found (Section 11.3). …

Figure 1Experimental arrangement for studying the photoelectric effect

What this figure shows. An evacuated glass (or quartz-windowed) tube houses two electrodes facing each other: a photosensitive metal plate C (the emitter/cathode) and a collector plate A (the anode), connected to the two terminals of a battery through a potentiometer (or rheostat) arrangement so the potential difference between A and C can be varied continuously in magnitude AND reversed in polarity (so A can be made either positive or negative with respect to C). Monochromatic light of a chosen frequency enters through a quartz window in the tube wall and falls on plate C, ejecting photoelectrons from its surface; those photoelectrons that reach plate A constitute the photoelectric current, read on a sensitive microammeter connected in series in the circuit, while a voltmeter connected across A and C reads the applied potential difference at each setting. The whole tube is evacuated so that the emitted electrons do not lose energy through collisions with air molecules on their way from C to A, and the source of light is mounted so that its intensity can a …

Figure 2Stopping potential versus frequency of incident light, for a given metal

What this figure shows. A graph is drawn with the frequency ν\nu of the incident light along the horizontal axis and the stopping potential V0V_0 along the vertical axis. For a single metal, the plotted points lie on a straight line of positive slope that does NOT pass through the origin: extended backward, it crosses the horizontal (frequency) axis at a positive value ν0\nu_0, the threshold frequency of that metal (where V0=0V_0=0), and crosses the vertical axis, when extended into negative ν\nu values, at a negative value equal to −ϕ0/e-\phi_0/e. If the same experiment is repeated with a second, different metal, a SECOND straight line is obtained, exactly PARALLEL to the first (same slope) but shifted sideways, crossing the frequency axis at that metal's own, different, threshold frequency -- so every metal gives a line of the identical slope but a different horizon …