Separate emitted-electron rate from stopping voltage

An event rate needs another assumption

The threshold relation predicts an energy ceiling, not how many electrons leave. To calculate a rate, this investigation supplies a 10% quantum yield above threshold: one emitted event per ten incident photons on average. This is an explicitly assumed teaching parameter, not a measured efficiency or universal property of metals.

At 8×10¹⁴ Hz, each photon carries about 5.301×10⁻¹⁹ J. A 2 mW beam therefore supplies approximately 3.773×10¹⁵ photons/s. Multiplying by 0.10 gives 3.773×10¹⁴ emitted electrons/s. The maximum kinetic energy is still approximately 1.309 eV, determined by 3.309−2 eV, not by the rate calculation.

Control one change at a time

Increasing power from 2 to 6 mW triples photon rate and the assumed emitted rate. It does not change photon energy, work function or ideal stopping voltage. Setting power to zero supplies no photons. The energy formula can still describe a hypothetical photon of that frequency, but there are no emitted electrons on which to perform a stopping-voltage measurement. The display explicitly distinguishes that empty-input case.

At the same 2 mW but 12×10¹⁴ Hz, each photon is more energetic, so the beam contains fewer photons per second. Under the deliberately fixed yield, emitted rate falls, while Kmax increases. A higher maximum energy and a lower count rate can therefore occur together. Real yields vary with frequency and surface conditions; the fixed-yield comparison is a controlled model, not a fitted prediction for a real material.

Reconstruct a charge current

If every emitted electron were collected, current magnitude would be e times the emitted rate. For the 8×10¹⁴ Hz,2 mW case this is approximately 60.45 µA. Collection losses or a retarding field would reduce the measured current. Emitted rate and collected rate are separate stages.

Evidence to request

To infer yield from measurements, ask for incident photon rate, illuminated area if intensity is supplied rather than total power, collection conditions, background and surface preparation. A current reading alone cannot determine all these quantities. This task is a virtual accounting exercise and never asks a learner to assemble a photoelectric apparatus.

Source and authorship

Reference for the physical relationship. Source checked 30 October 2026. The explanations, numerical cases, questions and diagrams here are original; reference material is not copied. Exact h,c,e follow NIST SI definitions.