Electron Emission

Why electrons stay bound

A metal owes its electrical conductivity to free electrons — negatively charged particles that move readily inside the metal. Although these electrons are free to roam through the interior, they cannot normally escape across the surface into the surrounding space. The constraint is electrostatic, not mechanical.

When an electron attempts to leave, the metal it abandons becomes momentarily positive at that point, and this positive surface charge pulls the departing electron straight back. In NCERT's description, the free electron is held inside the metal surface by the attractive forces of the positive ions. An electron can therefore emerge only if it is first supplied enough energy to overcome this attractive pull.

It helps to be precise about the sense in which these electrons are "free." NCERT's Points to Ponder stresses that free electrons move inside the metal in a roughly constant potential — they are free to wander within, but they are not free to move out. Crossing the surface requires additional energy. This is the conceptual hinge of the whole chapter: conduction (motion inside) and emission (escape across the surface) are governed by entirely different energy conditions, and the emission condition is what the work function quantifies.

Historically, the very existence of this emission was the clue that revealed the electron itself. Around 1887 it was found that certain metals, when irradiated by ultraviolet light, emitted negatively charged particles with small speeds, and that certain metals, when heated to high temperature, did the same. The charge-to-mass ratio of these particles matched that of cathode-ray particles, which led J. J. Thomson in 1897 to identify them all as electrons — universal constituents of matter. The phenomena we now classify as emission types were thus the experimental ground on which the electron was discovered, and the energy bookkeeping of their escape is what the rest of this page develops.

Work function and the energy barrier

A certain minimum amount of energy must be supplied to an electron to pull it out from the surface of the metal. NCERT names this quantity directly: the work function is the minimum energy required by an electron to escape from the metal surface. It is generally denoted by $\varphi_0$ and measured in electron volts.

Two features of the work function are decisive for problem-solving. First, $\varphi_0$ depends on the properties of the metal and the nature of its surface — it is an intrinsic material constant, not something the experimenter sets. Second, it is the least energy required: the free electrons in a metal do not all carry the same energy, and the work function is the energy needed by the most loosely held electrons among them. More tightly bound electrons need more.

The reason for that spread is worth pinning down, because it is exactly what the word "minimum" encodes. Free electrons in a metal do not all share a single energy; like molecules in a gas they have an energy distribution at any given temperature. Consequently the energy an electron needs to come out differs from electron to electron — those already sitting at higher energy need only a little more, those lower down need a great deal more. The work function is defined as the least energy any electron requires, so it corresponds to the electrons at the very top of that distribution. This is why a single number, fixed by the metal, can stand for the surface barrier even though individual electrons escape with a range of leftover energies.

The electron-volt unit

Work functions are quoted in electron volts because joules are inconveniently small at atomic scales. One electron volt is the energy gained by an electron when it is accelerated through a potential difference of 1 volt. Since the work done in moving a charge $q$ through a potential difference $V$ is $qV$, the electron volt follows from the elementary charge:

$$1\ \text{eV} = e \times 1\ \text{V} = 1.602\times10^{-19}\,\text{C} \times 1\,\text{V} = 1.602\times10^{-19}\ \text{J}.$$

This unit is commonly used in atomic and nuclear physics. A work function of a few electron volts therefore corresponds to a few times $10^{-19}$ joule — a number you will convert constantly when computing threshold frequencies and stopping potentials.

The same elementary charge that defines the electron volt also connects emission to measurable potentials elsewhere in the chapter. When a stopping potential $V_0$ just halts the most energetic photoelectrons, the energy relation is $K_{\max} = eV_0$; the appearance of $e$ here is the identical $1.602\times10^{-19}\ \text{C}$ that converts volts to joules. Treating the electron volt as "the charge $e$ times one volt" therefore keeps the units transparent across the work function, the stopping potential, and Einstein's equation alike.

The four emission processes

The minimum energy for electron emission can be delivered to free electrons by several distinct physical processes. NCERT §11.2 lists three; standard NEET treatments add secondary emission as a fourth. In every case the underlying requirement is identical — the electron must acquire energy at least equal to $\varphi_0$ — only the energy source differs.

Thermionic emission supplies the escape energy as heat. By suitably heating the metal, sufficient thermal energy is imparted to the free electrons to enable them to come out of the surface. The NIOS module notes the same point: in thermionic emission, electrons gain energy from thermal energy. This is the principle behind a heated cathode in vacuum tubes.

Field emission (also called cold-cathode emission) relies on a very strong electric field — of the order of $10^{8}\ \text{V m}^{-1}$ — applied to the metal, which pulls electrons out directly, as happens in a spark plug. No heating is required; the field itself does the work of extraction.

Photoelectric emission occurs when light of suitable frequency illuminates the metal surface, and electrons are emitted. These light-generated electrons are called photoelectrons. This process is the gateway to the rest of the chapter, where it is shown that a threshold frequency exists below which no emission occurs, however intense the light. The phenomenon was first noticed by Hertz in 1887 during his electromagnetic-wave experiments, and was studied in detail by Hallwachs and Lenard between 1886 and 1902 — it is the one emission process whose detailed laws NEET tests most heavily.

Each of these three processes appears in the NCERT summary as a single unified statement: energy greater than the work function, required for electron emission from the metal surface, can be supplied by suitably heating the metal, or by applying a strong electric field, or by irradiating it with light of suitable frequency. The emphasis falls on the common requirement — the energy must exceed $\varphi_0$ — with the three methods differing only in how that energy is delivered.

Secondary emission takes place when fast-moving electrons or other particles strike the metal surface and transfer enough of their kinetic energy to knock further electrons out. While NCERT §11.2 explicitly lists only the first three, secondary emission is a standard fourth category in the broader treatment of how the escape energy can be delivered. The energy source here is the kinetic energy of an incoming projectile rather than heat, field, or light.

Work-function values and threshold

Because the work function is the energy a photon must at least match for photoemission, it directly fixes the photoelectric threshold frequency $\nu_0$. When the incident energy exactly equals $\varphi_0$, the electron just escapes with zero kinetic energy, so $\varphi_0 = h\nu_0$, giving $\nu_0 = \varphi_0 / h$. A metal with a larger work function therefore demands a higher threshold frequency before emission can begin.

The NIOS module tabulates representative values. They show the trend that alkali-type metals such as sodium and potassium have low work functions — and therefore respond even to lower-frequency light — while transition metals such as iron and nickel sit much higher.

Values are reproduced from the NIOS Table 25.1. They make the comparison logic of NEET emission questions concrete: a photon can liberate an electron only from a metal whose work function does not exceed the photon's energy. A 2.2 eV photon, for instance, can free electrons from caesium ($\varphi_0 = 2.14$ eV) but not from sodium ($\varphi_0 = 2.75$ eV in the NEET 2023 data).

This is also why NCERT records that different metals respond to different parts of the spectrum. Metals such as zinc, cadmium and magnesium, with higher work functions, respond only to short-wavelength ultraviolet light, whereas the alkali metals — lithium, sodium, potassium, caesium and rubidium — have work functions low enough to be sensitive even to visible light. The table above is simply the quantitative version of that qualitative split: a small $\varphi_0$ means a small $\nu_0$, which means lower-frequency (longer-wavelength) light is already energetic enough to cause emission.

For NEET, the practical upshot is a fast decision rule. Convert the incident energy and every candidate work function into the same unit, then keep only the metals whose $\varphi_0$ is less than or equal to that incident energy. No emission occurs from a metal whose work function exceeds the supplied energy, no matter how intense the source — intensity changes the number of available quanta, not the energy each one carries. This single inequality, $E_{\text{incident}} \ge \varphi_0$, is the heart of every work-function comparison question.