Part of PH-01 — Dual Nature of Radiation & Matter

PH-01 Ten-Sentence Complete Recap

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The photoelectric effect is the emission of electrons from a metal surface when light of frequency at or above the threshold frequency ν_{0} strikes it. Einstein explained this in 1905 using the photon concept: each photon of frequency ν carries energy E = hν, and gives all this energy to one electron; the excess beyond the work function φ becomes the electron's maximum kinetic energy: KE_max = hν − φ. The stopping potential V0V_{0} = (hν − φ)/e is the key measurable quantity: it depends only on frequency, not intensity; this is the most tested concept in NEET from this chapter. Intensity of light controls only the number of emitted photoelectrons per second (the photocurrent), because intensity equals the number of photons per second, and more photons means more electron-photon collisions. The graph of KE_max vs frequency is a straight line with universal slope h; the graph of V0V_{0} vs frequency also gives a universal slope of h/e; both graphs have x-intercept at ν_{0} (metal-specific) and different metals give parallel lines. Photons have energy E = hν = hc/λ, momentum p = h/λ, zero rest mass, and always travel at c; the practical shortcut E(eV) = 1240/λ(nm) is essential for NEET speed. In 1924, de Broglie extended wave-particle duality to matter: every particle with momentum p has an associated matter wavelength λ = h/p, with heavier particles having shorter wavelengths at the same speed or accelerating potential. For an electron accelerated through V volts, this gives the shortcut λ = 1.227/√V nm — valid only for electrons. The Davisson-Germer experiment (1927) confirmed de Broglie's hypothesis by observing electron diffraction from a nickel crystal at 54 V, with the measured diffraction pattern matching the predicted wavelength to within 1%. Together, the photoelectric effect (radiation as particle) and electron diffraction (matter as wave) establish the principle of wave-particle duality — a cornerstone of modern quantum mechanics.

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