Dual Nature of Radiation and MatterNEET Physics · Class 12 · NCERT Chapter 11

You can expect 1 to 2 questions in NEET 2027. The chapter is small but reliable. Common asks: stopping potential vs frequency graph, KE_max calculation from Einstein's equation, de Broglie wavelength of an electron through a potential V, and photon momentum.

When light of high enough frequency strikes a metal surface, electrons are ejected. The ejected electrons are called photoelectrons. Below a threshold frequency f_0, no electrons are ejected no matter how intense the light. Above f_0, even very weak light ejects them instantly. Classical wave theory could not explain this; Einstein's photon idea did.

Work function W_0 is the minimum energy needed to free an electron from a metal's surface. Different metals have different W_0. Caesium has a low W_0 (about 2 eV); platinum is much higher (about 6.4 eV). W_0 = h f_0, where f_0 is the threshold frequency.

h f = W_0 + KE_max. The photon's energy h f goes to overcoming the work function W_0 and giving the electron kinetic energy KE_max. Below f = f_0, h f is less than W_0 and no electrons come out.

V_0 is the smallest reverse voltage that stops the most energetic photoelectrons from reaching the collector. e V_0 = KE_max = h f - W_0. V_0 vs f is a straight line: slope = h / e (universal), x-intercept = f_0 (depends on metal).

Saturation photo-current rises linearly with intensity (more photons → more electrons). It is independent of frequency once above f_0. Stopping potential rises linearly with frequency and is independent of intensity.

lambda = h / p = h / (m v). Every moving particle has a wave nature, with wavelength inversely proportional to momentum. For a tennis ball, λ is far too small to detect. For an electron, it is comparable to atomic spacings, so it can show diffraction.

lambda = h over root (2 m e V) = 12.27 over root V angstroms (when V is in volts). For 100 V: lambda ≈ 1.23 angstrom. This was confirmed by Davisson and Germer's electron diffraction experiment.

Electrons accelerated through 54 V were scattered by a nickel crystal and showed a clear diffraction peak at 50°, exactly as predicted by Bragg's law for wavelength 1.67 angstrom. This matched the de Broglie prediction and proved electrons behave as waves.

Classical waves cannot explain three things: existence of a threshold frequency, KE_max independent of intensity, and the instantaneous ejection of electrons. Einstein resolved all three by treating light as discrete photons of energy h f, each interacting one-on-one with one electron.