Topic 1 of 7
Evidence for photons
Light produces interference and diffraction patterns, but it also transfers energy in individual quanta. A successful explanation must account for both kinds of evidence.
In the photoelectric effect, electrons can leave a material when it absorbs suitable electromagnetic radiation. For a given surface there is a threshold frequency: below it, increasing ordinary illumination does not cause emission. Above it, emission is possible even with weak illumination.
A photon is one quantum of electromagnetic radiation. Its energy depends on frequency:
Here h is the Planck constant, 6.63 × 10-34 J s. At fixed frequency, higher intensity means more incident photons per second for a fixed illuminated area. It does not increase each photon's energy.
Compare frequency and intensity separately
Consider a surface with supplied threshold f0 = 5.00 × 1014 Hz. Keep the surface, geometry and collection conditions unchanged. The comparisons below use the ordinary single-photon model and, above threshold, conditions without saturation.
| Frequency | Illumination | Photoelectric result |
|---|---|---|
| 4.00 × 1014 Hz | Lower intensity | No emission: insufficient energy per photon. |
| 4.00 × 1014 Hz | Higher intensity | Still no emission in this model. |
| 6.00 × 1014 Hz | Lower intensity | Emission is possible. |
| 6.00 × 1014 Hz | Higher intensity | The emission rate can increase. |
Below the threshold: greater intensity is insufficient
Compare frequencies while holding the material and collection conditions fixed. The arrows show incoming photons and, where possible, outgoing electrons. Icon counts do not specify an efficiency or a measured rate.
Above the threshold: emission is possible
Compare frequencies while holding the material and collection conditions fixed. The arrows show incoming photons and, where possible, outgoing electrons. Icon counts do not specify an efficiency or a measured rate.
The threshold supports quantised energy exchange: adding more photons whose individual energies are too small does not meet the single-photon condition. This does not remove the wave evidence from interference and diffraction. Nor does it claim that one ordinary single-photon model covers arbitrarily intense fields.
The work function is an energy
The work function, written here as Φwork, is the minimum energy needed to remove an electron from the specified surface. At threshold:
= (6.63 × 10-34)(5.00 × 1014)
= 3.315 × 10-19 J
= 2.07 eV
One electronvolt is the energy gained by a particle of charge magnitude e accelerated through a potential difference of 1 V. Thus 1 eV = e × 1 V = 1.60 × 10-19 J using the supplied elementary charge. An eV is an energy unit, not a voltage. Φwork is measured in joules; it is distinct from magnetic flux Φ measured in webers.
Worked photon calculation
Energy, wavelength and momentum
An optical frequency of order 5 × 1014 Hz with h of order 7 × 10-34 J s suggests a few times 10-19 J per photon: a few eV. Expect a wavelength of a few hundred nanometres and momentum of order 10-27 kg m/s.
For f = 6.00 × 1014 Hz, use c = 3.00 × 108 m/s in vacuum:
E = hf = 3.978 × 10-19 J
E = (3.978 × 10-19)/(1.60 × 10-19)
= 2.48625 eV ≈ 2.49 eV
A photon has zero rest mass but nonzero momentum. Its momentum points along propagation, with magnitude:
= 1.326 × 10-27 kg m/s
≈ 1.33 × 10-27 N s
The non-relativistic formula p = mv for a massive particle is not a way to set photon momentum to zero. Check that energy divided by speed has momentum units.
A monochromatic beam with supplied power 1.989 µW at this frequency carries P/E = 5.00 × 1012 photons/s. That incident photon rate is not automatically a recorded electron rate: absorption, emission and collection efficiencies matter.