☰ Contents · Physics

Origins of quantum physics, photoeffect

Lessons 34–35 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
35

The photoelectric effect. Photons

Textbook: pp. 137–141
GoalKnow the laws of the external photoelectric effect, Einstein's equation hν = A + E_k and the red limit; use them in problems and distinguish the internal photoeffect.
New words
photoelectric effect · fotoeffektwork function · chiqish ishistopping voltage · yopuvchi kuchlanishphoton · foton
Explanation

The external photoelectric effect is the emission of electrons from a substance under the action of light. Experiments show: the saturation photocurrent is directly proportional to the light flux; the maximum kinetic energy of photoelectrons depends not on intensity but linearly on frequency (E_k max = eU_stop); each substance has a minimum frequency ν_min below which no effect occurs however strong the light is; the effect is inertialess. Wave theory could not explain this, but Einstein (1905) treated light as a stream of photons, each giving its whole energy hν to one electron: hν = A + E_k max, where A is the work function. Hence the red limit is ν_min = A/h, λ₀ = hc/A; stronger light means more photons and a larger current, but the energy of each photon is unchanged. The slope of the graph U_stop(ν) equals h/e, which allows h to be measured. In the internal photoeffect electrons in a semiconductor are freed by light and the conductivity inside the material increases (photoresistor).

Worked examples
Light of λ = 400 nm falls on a cathode with work function A = 2 eV: hν = 1240/400 = 3.1 eV, E_k max = 3.1 − 2 = 1.1 eV, stopping voltage U_stop = 1.1 V; the red limit is λ₀ = 1240/2 = 620 nm.
In an experiment U_stop = 0.48 V at ν₁ = 6·10¹⁴ Hz and 2.14 V at ν₂ = 10¹⁵ Hz. The slope ΔU/Δν = 1.66/(4·10¹⁴) ≈ 4.15·10⁻¹⁵ V·s = h/e, so h ≈ 4.15·10⁻¹⁵·1.6·10⁻¹⁹ ≈ 6.6·10⁻³⁴ J·s.
Class activity

Look at a calculator or watch with a solar cell: cover it with your hand and it stops working, an example of the internal photoeffect. Never look directly at the Sun and do not experiment with lasers or ultraviolet lamps.

Practice
1
What is the red limit of the photoeffect?
2
Photon energy is 5 eV and the work function 3 eV. What is E_k max in eV?
3
The work function is 3.1 eV. What is the red limit in nm? (hc = 1240 eV·nm)
4
Why does even strong light below the red-limit frequency not emit electrons?