Part 1 — The Photoelectric Effect (Chapters 1–3)

The photoelectric effect is the emission of electrons from a metal surface under irradiation by light of sufficiently high frequency. The phenomenon was discovered by Hertz (1887) and studied systematically by Lenard, whose experimental observations posed a fundamental challenge to classical wave theory of light. Classical theory predicted that any frequency of light, given enough intensity and time, should eject electrons — but experiments showed this was wrong. Emission was instantaneous even at low intensity (if ν ≥ ν_{0}), and no emission occurred below ν_{0} regardless of intensity.

Einstein resolved this in 1905 by treating light as photons each carrying energy E = hν. His photoelectric equation, KE_max = hν − φ, explained every observation: the threshold exists because a single photon must have hν ≥ φ; KE_max depends on ν because each photon gives exactly hν to one electron; intensity controls the number of photons per second, hence the number of ejected electrons per second (photocurrent), not the energy per electron. Einstein received the Nobel Prize for this in 1921.

Key formulae for NEET: KE_max = hν − φ; e$V_{0}$ = KE_max; ν_{0} = φ/h; λ_{0} = hc/φ = 1240/φ(eV) nm. The stopping potential $V_{0}$ = (hν − φ)/e in volts equals KE_max in eV numerically — this is the fastest path to answers.

Part 2 — Photon as a Particle (Chapter 4)

The photon model attributes particle properties to light. Each photon has: energy E = hν = hc/λ [ML^{2}$$T^{-2}]; momentum p = h/λ = E/c [M$LT^{-1}$]; rest mass = 0; speed = c in all frames. The fact that photons carry momentum was confirmed by the Compton effect (1923). NEET commonly tests photon energy calculations using the 1240 eV·nm shortcut and momentum using p = h/λ.

The saturation current in a photoelectric experiment is proportional to the rate of photon absorption: I_sat = neA where n = photon flux (photons/s/$m^{2}$). Doubling intensity doubles n, doubles I_sat, leaves $V_{0}$ unchanged.

Part 3 — de Broglie Hypothesis and Matter Waves (Chapters 5–6)

Building on Einstein's light-as-particle idea, de Broglie in 1924 proposed the reverse: if waves (light) can act as particles, perhaps particles can act as waves. He assigned wavelength λ = h/(mv) = h/p to every moving particle. This was a bold hypothesis with no direct experimental support at the time.

Experimentally confirming it required detecting diffraction — the quintessential wave behaviour. Davisson and Germer (1927) achieved this by observing diffraction maxima when electrons scattered off a nickel crystal lattice. The lattice spacing (~0.215 nm) acted as a diffraction grating for electrons with λ ~ 0.167 nm. The agreement between predicted and measured λ confirmed de Broglie's formula.

Key NEET formulae: λ = h/√(2m·KE); λ = h/√(2mqV); λ_electron = 1.227/√V nm; thermal λ = h/√(3mkT). Mass scaling: at same V, λ ∝ 1/√m (assuming same charge). Practical consequence: the electron microscope exploits the sub-nanometre wavelength of accelerated electrons to achieve resolution far beyond optical microscopes.