Dual Nature of Radiation and Matter — NEET Notes

Electron emission — four ways out of a metal

Metals are full of free electrons. They move around inside the lattice freely enough to conduct electricity, but they cannot leave the metal of their own accord. The reason is electrostatic: any electron that escapes leaves behind a positive surface charge that pulls it back. To get an electron permanently out of the metal, you must supply it with a definite minimum amount of energy — enough to overcome this binding pull. That minimum energy is the work function, denoted φ₀ and measured in electron volts (eV). One electron volt is the energy an electron gains when accelerated through one volt, equal to 1.602 × 10⁻¹⁹ joules. The work function is a property of the metal and the condition of its surface: caesium has φ₀ ≈ 2.14 eV, sodium 2.3 eV, potassium 2.3 eV, zinc 3.4 eV, iron 4.8 eV, nickel 5.9 eV.

NCERT lists three physical processes that can supply this energy; a fourth — secondary emission — is recognised in advanced texts but uses the same energy budget. Together they exhaust the routes by which an electron can exit a metal surface.

Photoelectric effect — Hertz and Lenard

The phenomenon was discovered by accident. In 1887, while running his celebrated electromagnetic-wave experiments, Heinrich Hertz noticed that the spark across his detector gap jumped more readily when the emitter electrode was illuminated by ultraviolet light from the arc lamp. Light, somehow, was helping charged particles escape. Hertz himself never pursued the lead — he was busy proving Maxwell right — but Wilhelm Hallwachs and Philipp Lenard spent the next fifteen years dissecting the effect. In 1888 Hallwachs showed that a negatively charged zinc plate lost its charge when bathed in ultraviolet light, and an uncharged zinc plate acquired a positive charge. After J. J. Thomson identified the electron in 1897, the picture clicked into place: ultraviolet light was knocking electrons out of the metal.

Lenard then assembled the apparatus that became canonical for this chapter — an evacuated tube with a photosensitive plate C (the emitter) and a collector plate A, both connected through a battery, microammeter, and voltmeter. By varying the polarity, intensity, and frequency, Lenard nailed down three observations that no wave theory could explain.

Experimental study — current, potential, frequency

The Lenard apparatus is simple but its three measurement loops produce every graph that NEET draws. A monochromatic beam from source S passes through a quartz window onto the photosensitive plate C. The battery sets a controllable potential difference V across C and A; a commutator lets the polarity reverse. The microammeter reads photocurrent; the voltmeter reads V. From this single setup, three graphs emerge that together encode the photoelectric effect.

The single most consequential measurement is the stopping potential. When plate A is made negative with respect to C, the electric field pushes electrons back. Only electrons energetic enough to climb against this potential reach the collector. As V becomes more negative, fewer electrons make it across; at some critical value V₀ — the stopping potential — even the most energetic electron is turned back, and the photocurrent drops to zero. That critical electron must have had kinetic energy equal to the work done against V₀:

KE_max = e V₀

Stopping potential converts to maximum kinetic energy

Two facts about V₀ are tested ruthlessly by NEET. First, V₀ depends on frequency, not intensity — raise the lamp's brightness ten-fold at fixed colour and V₀ does not shift. Second, V₀ rises linearly with ν above ν₀; the slope of the V₀-vs-ν graph is exactly h/e, the same for every metal, while the x-intercept ν₀ varies from metal to metal. Millikan spent a decade trying to disprove Einstein with this graph and ended up proving him right in 1916 — and measuring Planck's constant to high precision in the process.

Why the wave picture failed

By 1900, Maxwell's equations had crowned light as an electromagnetic wave. Interference, diffraction, polarisation — all yielded to wave theory. Yet that same wave picture made three predictions about photoelectric emission, every one of them contradicted by Lenard's data.

The wave picture was not wrong about everything — interference and diffraction still demanded waves. But the photoelectric effect was telling physicists that, in its interaction with matter, light came in discrete energy packets. A revolution was required.

Einstein's photoelectric equation

That revolution arrived in 1905. In one of three papers published in his "miracle year", Albert Einstein proposed that the energy of electromagnetic radiation is not spread continuously over the wavefront but bundled into discrete quanta, each of energy hν, where h is Planck's constant and ν is the frequency of the light. In the photoelectric process, a single electron absorbs a single quantum. If that quantum's energy exceeds the work function, the electron escapes; the excess appears as kinetic energy.

hν = φ₀ + KE_max = φ₀ + eV₀

Einstein's photoelectric equation — Nobel Prize 1921

From this single line, every Lenard observation falls out cleanly. Since KE_max = hν − φ₀, the maximum kinetic energy depends only on frequency, not intensity — that is exactly what experiment shows. For emission to occur at all, hν must exceed φ₀; rearranging gives the threshold frequency ν₀ = φ₀/h. Below ν₀, even infinite intensity cannot eject an electron, because intensity governs the number of quanta arriving, not the energy of each. And because the basic process is the absorption of one photon by one electron, it happens essentially instantaneously — no need to wait for the wavefront to "build up" energy.

Combining with KE_max = eV₀ gives the master equation for the stopping-potential graph:

V₀ = (h/e) ν − (φ₀/e)

Slope h/e (universal), intercept −φ₀/e (metal-specific)

This is the equation Millikan tested across a decade of measurements. Slope of the V₀-vs-ν line gave him a value of h consistent with Planck's value 6.626 × 10⁻³⁴ J·s — derived from a totally unrelated experiment on black-body radiation. Independent measurements of the same constant from two unrelated phenomena: that was the moment the photon hypothesis stopped being heresy and became orthodoxy.

Particle nature of light — the photon

If light carries energy in discrete quanta, can each quantum be regarded as a particle? Einstein had already shown that a quantum of frequency ν has energy hν. Using relativistic energy-momentum for a massless particle moving at c, he then derived its momentum as p = E/c = hν/c = h/λ. A definite energy plus a definite momentum is the signature of a particle. The quantum was given a name — the photon — by Gilbert Lewis in 1926, and its particle status was sealed in 1924 when A. H. Compton observed X-rays scattering off electrons exactly as a billiard-ball collision would predict, conserving energy and momentum photon-by-photon.

The photon's properties are tested in nearly every NEET paper and must be at fingertips.

Two further rules round out the photon picture. In any photon-particle collision (such as Compton scattering), total energy and total momentum are conserved, but the number of photons need not be — a photon can be absorbed, or a new one created. And the intensity of light at a given frequency is simply the number of photons crossing unit area per unit time; raising intensity does not raise a single photon's energy by even a fraction of a per cent.

Wave nature of matter — de Broglie's hypothesis

If light, which everyone had thought was a wave, also behaves like a particle, then symmetry demands the converse — particles, the everyday electrons and protons of matter, should also behave like waves. That was the bet placed by a young French physicist, Louis Victor de Broglie, in his 1924 PhD thesis. His argument was almost embarrassingly simple. For a photon, p = h/λ. Why not assume the same relation holds for any particle, with the wavelength on the left and the momentum on the right? De Broglie's thesis examiners almost rejected the manuscript; Einstein, asked for a second opinion, recognised genius and ensured the doctorate was awarded. Five years later de Broglie had a Nobel Prize.

λ = h / p = h / mv

de Broglie wavelength — bridges particle (p) and wave (λ)

The formula is universal. Plug in the momentum of any particle and out comes a wavelength. For a cricket ball (m = 0.15 kg, v = 30 m/s) the de Broglie wavelength comes out to roughly 10⁻³⁴ m — ten quadrillion times smaller than a proton, so utterly unobservable that the ball's wave character is invisible. For an electron (m = 9.11 × 10⁻³¹ kg) accelerated through even a few volts, λ falls in the angstrom range — comparable to atomic spacings in crystals. That is the regime in which matter waves stop being a thought experiment and start producing measurable diffraction.

For a particle of kinetic energy E (non-relativistic), the formula has several useful equivalent forms that NEET problems exploit:

For an electron specifically, a numerical shortcut saves time in the exam. Substitute m = 9.11 × 10⁻³¹ kg and q = e = 1.602 × 10⁻¹⁹ C; the wavelength in angstroms reduces to a one-line formula.

Davisson-Germer — matter waves measured

De Broglie's relation was a hypothesis until 1927. That year, two experiments — Davisson and Germer in the United States, and G. P. Thomson independently in Britain — confirmed it directly by showing that electrons diffract from a crystal exactly as predicted. The Davisson-Germer setup is the canonical version for NEET.

In their experimental tube, a heated filament F emits electrons that pass through metal diaphragms with slits, forming a collimated beam. The beam is accelerated through a known potential V, then directed perpendicular onto a single nickel crystal. A movable detector measures the intensity of electrons scattered at any chosen angle θ. The setup is essentially an electron analogue of Bragg X-ray diffraction.

The decisive run was almost an accident. When their nickel target cracked during repairs, Davisson and Germer re-heated it in hydrogen and vacuum — a process that fused the polycrystalline target into a few large single-crystal facets. When measurements resumed, a sharp intensity peak appeared at θ = 50° for electrons accelerated through 54 V. The peak's existence demanded constructive interference — and the wavelength derived from Bragg's condition matched the de Broglie value h/p almost exactly.

The experiment did more than confirm a formula. It established matter waves as a measurable physical reality, opened the field of electron diffraction, and within a few years made possible the electron microscope — an instrument whose resolution beats an optical microscope by four orders of magnitude precisely because λ for accelerated electrons is so much shorter than visible light. Davisson shared the 1937 Nobel Prize with G. P. Thomson.