Фотоэффект

Physical Background

Using a vacuum phototube where almost no particles of gas may influence the flow of electrons we can study how light incident onto the cathode (photocathode) may liberate (kick out) electrons from the surface of the photocathode. The flow of electrons can be driven by voltage on the anode – the negative voltage (stopping voltage) repels negatively charged electrons so that they cannot reach the anode and no current flows through the phototube. The positive voltage on the anode accelerates electrons moving towards the anode and higher photocurrent can be observed. The potential energy in the electric field between the cathode and the anode (the work of the electrical force) is transformed to the kinetic energy of electrons, and through the stopping voltage value U0 we can measure the kinetic energy of electrons Ek

Ek = e |U0|                                         (1)

where e = 1,602.10−19 C is the charge of electron in the absolute value. Two convenient units for Ek are used: a joule (J), or an electronvolt (eV) where the value corresponds to the absolute value of the stopping voltage in volts.

Fig. 1

Fig. 1: Visualisation of the photoelectric effect with an applet (http://PhET.colorado.edu). Electrons emitted (kicked out) from the photocathode by the incident violet light (400 nm) are blocked by the negative voltage (stopping voltage −1,40 V) on the anode so that they cannot reach the anode and no current is measured.

We can change the voltage between the cathode and the anode using an external voltage source to study the volt-ampere characteristics of the vacuum phototube. The physical background and the stopping voltage method described above can be visualised and explained with the usage of PhET applet ‘Photoelectric effect’ (see the Fig. 1), accessible for free at


requiring only the JAVA Runtime Environment (JRE) installed on your computer.

There were several interesting characteristics observed with the photocurrent:

  1. The greater light intensity is incident, the higher photocurrent is measured (as expected).
  2. The stopping voltage does not depend on the light intensity (surprising).
  3. The stopping voltage depends on the frequency of the incident electromagnetic radiation (simple dependence U0 = U0(f) = U0(1/λ) was surprising – see the Fig. 2a).
  4. No photocurrent can be observed for frequencies less than one certain threshold frequency f0 (wavelengths greater than the corresponding threshold wavelength λ0), determined by the material of the photocathode, and regardless of the light intensity (surprising).
  5. Saturation of the photocurrent occurs for higher positive voltages on the anode. The saturation photocurrent is determined by the intensity of light. (See the Fig. 2b.)

Fig. 2

Fig. 2: a) simple dependence kinetic energy of electrons vs. frequency of incident elmg. radiation, b) typical V-A characteristics with the zero photocurrent for U < U0 and the saturation of photocurrent (the photocurrent does not change for higher positive voltages).

The wavelength λ (the threshold wavelength λ0) corresponds to the frequency f (the threshold frequency f0)

f = c/λ, f0 = c/λ0                                       (2)

where c = 3.108 m/s is the vacuum light velocity. The characteristics II–IV were difficult to explain easily but the experimental dependence Ek(f) = eU0(f) was simply a linear function of the frequency f>f0

Ek(f) = eU0(f) = K (ff0)                         (3)

where K is the coefficient or the slope as well (see the figure 3).

Fig. 3

Fig. 3: Observed simple dependence electron energy vs. frequency – linear function (3).

All the characteristics II–IV and the experimental dependence (3) were explained by Albert Einstein at once in 1905 when A. Einstein used the Max Planck’s quantum hypothesis that light is represented by quanta (particles, named photons since 1926) with the energy Ephoton = hf where h = 6,63.10−34 J.s is the Planck constant. Then for K = h we can explain the dependence (3) as the law of conservation of energy

Ek(f) = eU0(f) = h (ff0) = h.fh.f0 = EphotonW ,           (4)

therefore the energy of a photon incident onto the photocathode
Ephoton = W + Ek                                       (5)

is transformed to the work function W = h.f0 necessary to kick the electron out of the photocathode and the rest is equal to the kinetic energy Ek of the electron. Thus, the threshold frequency is related to the work function that is determined by material of the photocathode.

In this explanation we consider interaction between two particles (a photon with sufficient energy and an electron, not an electromagnetic wave with a particle) where the energy-conservation law remains valid.