Light incident on a suitable material can eject electrons. In this experiment, light illuminates a metal cathode inside an evacuated photocell. We infer electron motion from the collected current.
Emission means electrons leave the surface. Detection means electrons arrive at the collector. A retarding field can prevent detection while emission continues.
The threshold frequency and the dependence of maximum electron energy on frequency challenged a simple classical wave explanation in which energy transfer would depend on light intensity. Einstein’s photon model accounts for these observations.
Frequency f counts oscillations per second (Hz). Wavelength λ is the distance between wave crests. In vacuum they obey c = fλ. Intensity is optical power per unit area.
Shorter wavelength means higher frequency. Convert nanometres to metres before calculating: 1 nm = 10⁻⁹ m. At 400 nm, f ≈ 7.49 × 10¹⁴ Hz.
For monochromatic light, photon arrival rate per unit area is intensity divided by hf. At a fixed frequency, more intensity means more photons. At fixed optical intensity, increasing frequency actually reduces photon flux. Current also depends on collection and conversion efficiency.
A photon is one quantum of electromagnetic energy. Its energy depends on frequency, not on how bright the source looks. The same colour can be delivered as a faint beam or a bright beam.
Using h = 6.62607015 × 10⁻³⁴ J s and c = 299792458 m/s gives energy in joules. Divide by e = 1.602176634 × 10⁻¹⁹ C to express the energy in electronvolts.
One electronvolt is the energy change of an elementary charge across one volt: 1 eV = 1.602176634 × 10⁻¹⁹ J. It is an energy unit, whereas a volt is a potential-difference unit.
The work function φ is the minimum energy needed to remove an electron from the material into vacuum. It depends on material and surface condition. A photon must supply at least this escape energy.
For our representative sodium surface, φ = 2.28 eV. A 450 nm photon supplies about 2.76 eV, leaving a maximum of about 0.48 eV for electron motion.
Electrons do not all escape with the same kinetic energy. Their initial states and energy losses differ. Einstein’s relation specifies the upper end of the emitted energy distribution; this is what stopping potential probes.
The ideal emission threshold occurs when the photon has just enough energy to overcome the work function. Below the threshold frequency, increasing intensity cannot produce emission within this single-photon model.
Emission requires f > f₀, equivalently λ < λ₀ for positive electron kinetic energy. Sodium’s representative threshold wavelength here is about 544 nm.
Multiphoton and other strong-field processes can occur outside the ordinary low-intensity photoelectric experiment. They are excluded from this model. Exactly at threshold the ideal maximum kinetic energy is zero.
A photon transfers its energy in one absorption event. Some energy is needed for escape; the remaining energy sets the maximum kinetic energy of an emitted electron.
Above threshold, increasing frequency increases Kmax. Increasing intensity at fixed frequency increases the number of absorption events but does not increase Kmax.
When hf < φ, the negative algebraic result signals that emission is energetically forbidden. It does not describe an emitted electron with negative kinetic energy. The workbench shows zero and a no-emission message.
A negative collector voltage produces an electric field that opposes electrons travelling from cathode to collector. Increase its magnitude until even the fastest electrons cannot cross.
Here e is the positive elementary-charge magnitude and Vₛ is the positive magnitude of the stopping voltage. The control displays signed collector voltage; the notebook records its magnitude.
Every sufficiently negative voltage also gives zero collected current. Only the boundary between nonzero and zero collection estimates stopping potential. Bracket that boundary instead of choosing an arbitrary zero-current voltage.
Photocurrent is collected charge per unit time. For emission above threshold, increasing intensity at fixed wavelength generally raises the saturation current. A retarding voltage rejects progressively more emitted electrons.
At sufficient collecting voltage, all available photoelectrons are collected in the ideal model. Increasing voltage further then produces no extra photoelectrons.
Its shape is illustrative. We assume constant conversion efficiency and a simple energy distribution. Actual curves depend on geometry, electron energies, electrode contact potentials, space charge and dark current. Only the ideal stopping boundary follows directly from Einstein’s relation.
Rearrange the energy equation to express stopping potential as a straight-line function of frequency. Use several frequencies with the same emitting surface.
The gradient m equals h/e, so h = em. The vertical intercept b equals −φ/e. With frequency in Hz, the gradient has units V s and h has units J s.
The chart uses scaled axis labels for readability. The fit converts its gradient back to V s before calculating h. If you calculate manually from the displayed axis, divide the graphical gradient by 10¹⁴.
Repeated readings reveal random scatter. Instrument resolution, wavelength bandwidth and calibration contribute uncertainty. A systematic voltage offset can shift the intercept even when the gradient looks reasonable.
Look for a pattern in residuals, repeat measurements, and report assumptions. A small difference from the accepted h does not by itself prove a precise or accurate measurement.
Its readings are generated from a model that already contains the accepted value of h. Fitting them practises measurement and analysis; it is not independent evidence for the value of h. In a physical lab, use the actual setup’s documented corrections and uncertainty budget.