KE vs Frequency
Parallel lines of slope h/e = 4.14 × 10⁻¹⁵ V·s — same slope, different intercepts per metal.
Key Notes
Maximum KE of photoelectrons varies LINEARLY with frequency: K_max = hf − φ.
Slope = h (Planck's constant). x-intercept = f₀ = φ/h. y-intercept (at f=0) = −φ.
Below threshold (f < f₀): K_max would be negative — physically means no emission.
Crucially: K_max does NOT depend on intensity. Same f and metal ⇒ same K_max regardless of how bright the light is.
This linearity was a key prediction of Einstein's photon theory — confirmed by Millikan's experiments.
Different metals: parallel lines (same slope h) but different intercepts (different φ).
Photon picture: each photon transfers its full energy hf to ONE electron. The electron uses φ to escape, keeps the rest as KE.
Formulas
K_max vs f (Einstein)
Linear in f; slope = h, intercept = −φ.
K_max in terms of V_s
Stopping potential gives K_max directly.
Threshold (K_max = 0)
Below this frequency, no photoemission.
Important Points
K_max depends on frequency, NOT on intensity. Bright dim red light gives no emission from a metal that responds only above blue.
Slope of K_max vs f is UNIVERSAL — Planck's constant h, independent of metal.
Doubling f doesn't usually double K_max — only if you start far above φ. The contribution −φ shifts everything.
Photoelectrons can have a RANGE of KEs (from 0 to K_max), depending on how deep in the metal they were and energy losses on the way out.
K_max measurable via stopping potential: V_s × e = K_max.
Linear K vs f and zero-time-delay together killed the classical wave-theory of photoemission.
KE vs Frequency notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.