Stopping Potential
eV_s = hf − φ — split view: I–V curve + V_s vs f plot with live point.
Key Notes
Stopping potential V_s is the retarding voltage (anode held NEGATIVE w.r.t. cathode) at which photoelectric current drops to ZERO.
At V = V_s, even the MOST energetic photoelectron (K = K_max) is just barely stopped: eV_s = K_max.
Stopping-potential equation: eV_s = hf − φ.
V_s is INDEPENDENT of intensity — depends only on frequency and metal.
Plotting V_s vs f: straight line with slope h/e and x-intercept f₀.
Slope h/e ≈ 4.136 × 10⁻¹⁵ V·s — same for all metals. Y-intercept (at f = 0): −φ/e — depends on metal.
Millikan's 1914 experiment measured V_s vs f for several metals — confirmed Einstein's equation and gave a precise value of h.
Formulas
Stopping potential
Maximum KE of photoelectrons = retarding work done by V_s.
Slope of V_s vs f
Universal — same for every metal.
Intercept on V_s axis (f = 0)
Negative — graph crosses below x-axis.
Threshold from intercept
x-intercept of V_s vs f line.
Important Points
V_s is what's MEASURED — K_max is INFERRED via eV_s.
V_s does not depend on the intensity of incident light. This was a key surprise to classical physicists.
All metals give parallel V_s-vs-f lines (same slope h/e, different intercepts).
The slope h/e from Millikan's data gave one of the most precise early measurements of Planck's constant.
If V is REVERSED to positive (anode + w.r.t. cathode), saturation current is observed.
Lab-trick: extrapolate the V_s-vs-f line — its x-intercept gives f₀, y-intercept gives −φ/e.
Stopping Potential 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.