Dual Nature of Radiation & Matter

The photoelectric effect is the emission of electrons from a metal surface when light of a high enough frequency shines on it. Discovered through careful experiments, it could not be explained by the wave theory of light and became one of the key clues that light has a particle nature. The emitted electrons are called photoelectrons.

The experiments revealed clear laws. First, emission occurs only if the frequency exceeds a certain minimum, the threshold frequency $\nu_0$ — below it, no electrons are emitted no matter how intense the light. Second, above threshold the number of photoelectrons (and hence the current) is proportional to the intensity, while the maximum kinetic energy of the electrons depends only on the frequency, not the intensity.

Third, the emission is instantaneous — electrons appear within nanoseconds of the light striking, with no time delay even at very low intensity. Each of these facts contradicts the wave model, which predicts that any frequency should eventually eject electrons given enough time and intensity, and that brighter light should give more energetic electrons.

To measure the electrons' energy, a reverse voltage is applied until the current just stops; this is the stopping potential $V_0$, related to the maximum kinetic energy by $eV_0 = K_{max}$. The stopping potential increases with frequency but is independent of intensity — a result that is central to NEET questions and directly demonstrates the particle behaviour of light.

Einstein explained the photoelectric effect by proposing that light comes in discrete packets of energy called photons, each carrying energy $E = h\nu$, where $h = 6.63\times10^{-34}\ \text{J s}$ is Planck's constant. A single photon is absorbed by a single electron in an all-or-nothing event, which immediately accounts for the instantaneous emission and the frequency threshold.

Some minimum energy, the work function $\phi$, is needed just to free an electron from the metal. Any photon energy beyond this appears as the electron's kinetic energy, giving Einstein's photoelectric equation: $h\nu = \phi + K_{max}$, or $K_{max} = h\nu - \phi$. The work function is related to the threshold frequency by $\phi = h\nu_0$, so emission occurs only when $h\nu > \phi$.

This single equation explains every observation. The kinetic energy rises linearly with frequency and is independent of intensity; below $\nu_0$ the photon simply lacks the energy to free an electron; and brighter light means more photons, hence more electrons but not more energetic ones. A graph of $K_{max}$ against $\nu$ is a straight line of slope $h$ and intercept $-\phi$ — a classic NEET graph.

The photon also carries momentum $p = \dfrac{h}{\lambda} = \dfrac{h\nu}{c}$, despite having no rest mass, confirmed by the scattering of X-rays off electrons (the Compton effect). So light shows a genuine dual nature: it propagates and interferes like a wave, yet exchanges energy and momentum in particle-like quanta. Which face it shows depends on the experiment — the central idea of this chapter.

If light waves can behave like particles, de Broglie proposed the converse: particles of matter can behave like waves. Every moving particle has an associated de Broglie wavelength $\lambda = \dfrac{h}{p} = \dfrac{h}{mv}$. This bold symmetry completed the idea of wave–particle duality and is the conceptual heart of this module.

The key feature is that the wavelength is inversely proportional to momentum. A fast or heavy particle has a tiny wavelength, while a slow, light particle has a larger one. This is exactly why we never notice the wave nature of everyday objects — a moving cricket ball has a de Broglie wavelength far too small to detect — but electrons, being very light, have measurable wavelengths.

For a charged particle accelerated through a potential difference $V$, the kinetic energy is $eV = \tfrac{1}{2}mv^{2}$, which gives a convenient form $\lambda = \dfrac{h}{\sqrt{2meV}}$. For an electron this reduces to the handy NEET shortcut $\lambda \approx \dfrac{12.27}{\sqrt{V}}\ \text{angstrom}$ (with $V$ in volts) — a result worth memorising for quick numericals.

de Broglie's idea was confirmed by the Davisson–Germer experiment, in which a beam of electrons was diffracted by a crystal, producing a pattern just like X-ray diffraction. Since diffraction is a wave phenomenon, this directly proved that electrons have a wave nature. Today, electron microscopes exploit the very short wavelength of fast electrons to resolve detail far finer than any light microscope — a powerful real-world payoff of matter waves.

It is worth gathering together the properties of the photon, the particle of light, because NEET tests them as a set. A photon has energy $E = h\nu$ and momentum $p = h\nu/c = h/\lambda$. It travels at the speed of light $c$ in vacuum and, crucially, has zero rest mass — it cannot exist at rest. Its energy and momentum depend only on the frequency (or wavelength) of the light.

Photons are electrically neutral, so they are not deflected by electric or magnetic fields, unlike electrons. In any interaction, total energy and total momentum are conserved. The intensity of a light beam is the number of photons crossing per unit area per unit time multiplied by the energy per photon — so a brighter beam of the same colour simply has more photons, each still of energy $h\nu$.

The deep lesson of this chapter is wave–particle duality: both light and matter exhibit wave and particle aspects, and which aspect appears depends on the experiment performed. Interference and diffraction reveal the wave side; the photoelectric and Compton effects reveal the particle side. No single experiment shows both at once, a complementarity that is itself examinable.

This duality marks the boundary of classical physics and the start of quantum ideas, leading on to the structure of the atom in the next chapter. For NEET, the practical skills are computing photon energy and momentum, applying $K_{max} = h\nu - \phi$, finding de Broglie wavelengths, and knowing which phenomena demonstrate the wave versus the particle nature — a compact, high-frequency cluster of questions.