Dual Nature of Matter and Radiation

Light shining on a metal surface ejects electrons. Classical wave theory failed to explain four observations:

Fact 1: Existence of threshold frequency (ν₀). Below ν₀, no electrons emerge — no matter how intense the light or how long you shine it.

Fact 2: Above threshold, KE_max depends on frequency, not intensity.

• Intense red light: many photons but no emission (if ν < ν₀).
• Weak UV: ejects electrons with measurable KE (if ν ≥ ν₀).

Fact 3: Above threshold, intensity affects current (number of electrons), not their KE.

Fact 4: Emission is essentially instantaneous (~10⁻⁹ s). Wave theory predicted minutes-long buildup.

Einstein's explanation (1905, Nobel Prize 1921): light comes in discrete quanta (photons) of energy E = hν. Each photon, on absorption, transfers all its energy to one electron.

Einstein's photoelectric equation:

KE_max = hν − φ

where φ = work function (minimum energy to liberate an electron from the metal). Threshold frequency: ν₀ = φ/h.

Stopping potential V_s is the reverse voltage that just stops the most energetic electrons:

eV_s = KE_max = hν − φ

A plot of V_s vs ν gives a straight line with:

• Slope = h/e (Planck's constant per electron charge — verifies h)
• y-intercept = −φ/e
• x-intercept = ν₀ (threshold frequency)

This experimental setup is how Millikan precisely measured h in 1916, confirming Einstein.

Common JEE/NEET pitfalls:

• The photon energy E = hν, NOT E = hc/λ unless asked in terms of wavelength. (Both are equivalent: ν = c/λ.)
• Wavelength threshold: λ₀ = hc/φ. Light with λ > λ₀ won't cause emission.
• Stopping potential is independent of intensity — only frequency matters.