Why Red Light Cannot Knock Electrons Out of Zinc, However Bright

A metal is full of free electrons, yet they do not simply fall out. They escape only when given enough energy — by heating, by a strong electric field, or by light. That last route, the photoelectric effect, reveals something surprising about the nature of light.

This part covers electron emission and work function, the key observations of the photoelectric effect, and its experimental study.

**Electrons are held inside a metal by the attraction of its positive ions, and the minimum energy needed to free one from the surface is the work function ${\varphi }_0$; for light, the matching minimum frequency is the threshold frequency ${\nu }_0=\frac{{\varphi }_0}{h}$.

Ways to supply the energy:

- Thermionic emission — heating the metal
- Field emission — a very strong electric field pulling electrons out
- Photoelectric emission — light of high enough frequency

Work function** is usually given in electron volts, where $1$ eV $=1.6\times 10^{-19}$ J. It depends on the metal and its surface: alkali metals such as cesium and potassium have low values, around $2$ eV.

Worked example. Cesium has ${\varphi }_0=2.14$ eV:

$${\nu }_0=\frac{{\varphi }_0}{h}=\frac{2.14\times 1.6\times 10^{-19}}{6.63\times 10^{-34}}\approx 5.2\times 10^{14}\text{ Hz},{\lambda }_0=\frac{c}{{\nu }_0}\approx 580\text{ nm}$$

Visible light up to yellow-green can free electrons from cesium. Zinc, with ${\varphi }_0$ about $4.3$ eV, has ${\lambda }_0\approx 290$ nm, in the ultraviolet.

An everyday example. The heated filament inside an X-ray machine's tube supplies its electrons by thermionic emission.

The substance. The work function belongs to the metal, not to the light — the same light can free electrons from one metal and not from another.

Ultraviolet light falling on a metal such as zinc ejects electrons from it, but below a certain frequency no electrons come out however bright the light is, while alkali metals respond even to visible light.

The observations grouped under this heading in the syllabus:

- Sparks jump a gap more readily when the electrodes are lit by ultraviolet light
- In an evacuated tube, ultraviolet light on one plate makes a current flow to a second plate, and the current stops when the light is removed
- A negatively charged zinc plate lit by ultraviolet light loses its charge, while a positively charged plate keeps it
- Below a certain frequency, no electrons are emitted, whatever the intensity
- Emission begins almost instantly, even in dim light

The emitted particles are electrons, called photoelectrons.

Worked example. A zinc plate lit by ultraviolet light loses a charge of $3.2\times 10^{-12}$ C:

$$n=\frac{q}{e}=\frac{3.2\times 10^{-12}}{1.6\times 10^{-19}}=2\times 10^7\text{ electrons}$$

An everyday example. A gold-leaf electroscope in a physics laboratory shows the effect directly: its leaves collapse when ultraviolet light shines on a negatively charged zinc disc fixed on top.

The substance. These observations tie emission to frequency, not intensity — a clue the wave theory of light cannot explain.

**In a photocell, photocurrent rises with light intensity and with collector potential up to a saturation value, and the reverse potential just large enough to stop the fastest electrons — the stopping potential $V_0$ — satisfies $e{V}_0=K_{max}$; $V_0$ grows with frequency but does not depend on intensity.

Set-up: an evacuated tube with an emitter plate and a collector, a quartz window, a variable potential and a microammeter.

Effect of intensity** at a fixed frequency above ${\nu }_0$: photocurrent is directly proportional to intensity, because more light ejects more electrons.

Effect of potential:

- A positive collector potential increases the current until all emitted electrons are collected — the saturation current
- A negative potential repels electrons; the current falls to zero at the stopping potential $V_0$
- For different intensities, saturation currents differ but **$V_0$ is the same

Effect of frequency:**

- $V_0$ increases linearly with frequency above ${\nu }_0$
- The graph of $V_0$ against $\nu$ has the same slope for every metal but cuts the frequency axis at each metal's own ${\nu }_0$

Worked example. A stopping potential of $1.5$ V means $K_{max}=1.5$ eV $=2.4\times 10^{-19}$ J, so

$$v_{max}=\sqrt{\frac{2K_{max}}{m}}=\sqrt{\frac{2\times 2.4\times 10^{-19}}{9.1\times 10^{-31}}}\approx 7.3\times 10^5{\text{ m s}}^{-1}$$

An everyday example. Light-beam sensors that stop a lift door from closing work on a closely related idea — a beam falling on a photosensor keeps a current flowing until someone interrupts it.

The substance. Brighter light gives more electrons, not faster ones — only a higher frequency raises $V_0$.