☰ Contents · Physics

Photon momentum and uses of the photoeffect

Lessons 36 · 1 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
36

Photon momentum. Light pressure. Technical uses of the photoeffect

Textbook: pp. 142–148
GoalKnow the photon momentum p = h/λ = E/c and light pressure p = I/c (absorbing), 2I/c (reflecting); explain technical uses of the photoeffect (photoresistor, solar cell, light-emitting diode).
New words
photon momentum · foton impulsilight pressure · yorug‘lik bosimisolar cell · quyosh batareyasilight-emitting diode · yorug‘lik diodi
Explanation

A photon has zero mass but has energy E = hν and momentum: from E = pc, p = E/c = hν/c = h/λ. Photons falling on a surface give it momentum, so light exerts pressure. For light of intensity I (W/m²) falling perpendicular to the surface, the pressure on a fully absorbing surface is p = I/c and on a fully reflecting surface p = 2I/c, because on reflection the photon's momentum changes by 2p. This pressure is tiny (sunlight near the Earth presses on an absorbing surface with about 4.5 μPa, a few millionths of a pascal); P. N. Lebedev measured it in 1900 with a delicate torsion balance, and it is now used in designs of lightweight solar-sail spacecraft. Technical uses of the photoeffect: a photoresistor's resistance falls when it is lit (light sensors, automation); a p–n junction solar cell converts light energy directly into electrical energy (one cell gives an emf of about 0.5 V, so cells are connected in series); in a light-emitting diode current in a p–n junction produces light by recombination of electrons and holes, and the colour depends on the semiconductor.

Worked examples
A photon with λ = 330 nm: p = h/λ = 6.6·10⁻³⁴/(3.3·10⁻⁷) = 2·10⁻²⁷ kg·m/s; its energy is E = pc = 2·10⁻²⁷·3·10⁸ = 6·10⁻¹⁹ J (≈ 3.75 eV).
Light of I = 900 W/m² falls perpendicular on a sail. On an absorbing surface p = I/c = 900/(3·10⁸) = 3·10⁻⁶ Pa, on a reflecting sail 2I/c = 6·10⁻⁶ Pa; for a sail of area 20 m² the force is F = pS = 6·10⁻⁶·20 = 1.2·10⁻⁴ N.
Class activity

Take a solar calculator or garden lamp and watch how it works with different lighting (shade, room, window). Do not look straight at the Sun and never point a laser pointer at eyes or people.

Practice
1
Write the formula for photon momentum in terms of wavelength.
2
A 50 cm² solar cell gives 40 mA from each cm². What is the total current in mA?
3
A photon has energy 9·10⁻¹⁹ J. What is its momentum? (c = 3·10⁸ m/s)
4
Why does a mirror produce twice the pressure of an absorbing surface?