{"id":333,"date":"2018-04-23T07:56:55","date_gmt":"2018-04-23T07:56:55","guid":{"rendered":"http:\/\/www.milq.info\/?page_id=333"},"modified":"2026-07-13T07:57:29","modified_gmt":"2026-07-13T05:57:29","slug":"74-was-spricht-gegen-die-erklaerung-des-photoeffekts-mit-der-wellentheorie-des-lichts","status":"publish","type":"page","link":"https:\/\/www.milq.info\/en\/74-was-spricht-gegen-die-erklaerung-des-photoeffekts-mit-der-wellentheorie-des-lichts\/","title":{"rendered":"What is the problem with using the wave theory of light to explain the photoelectric effect?"},"content":{"rendered":"
<\/div>

The photoelectric effect shows a number of features that make an explanation in terms of the classical wave theory of light appear difficult. According to the classical theory of the free electron gas, the metal electrons are free particles acted on by the force<\/p>\n

\"F = -e\,E = -e\,E_0 \cos\omega t\"<\/p>\n

(where \"E\" = electric field strength, \"\omega\" = angular frequency of the incident wave).<\/p>\n

The equation of motion of an electron is then:<\/p>\n

\"m\ddot{x} = -e\,E_0 \cos\omega t\" (1)<\/p>\n

with the solution<\/p>\n

\"x(t) = \dfrac{e\,E_0}{m\,\omega^2}\cos\omega t\" (2)<\/p>\n

The decisive quantity here is the kinetic energy that the electron gains from the incident wave. The higher it is, the more easily the electron can escape from the metal. Differentiating equation (2) and substituting the result into the expression for the kinetic energy gives:<\/p>\n

\"E_{\mathrm{kin}} = \tfrac{1}{2}\,m\,\dot{x}^2(t) = \tfrac{1}{2}\,m\left(\dfrac{e\,E_0}{m\,\omega}\right)^2\sin^2\omega t\" (3)<\/p>\n

The electron has its maximum kinetic energy when the sine takes the value 1:<\/p>\n

\"E_{\mathrm{kin,max}} = \dfrac{1}{2}\,\dfrac{e^2 E_0^2}{m\,\omega^2}\" (4)<\/p>\n

That is: according to the classical theory the maximum energy of an electron is proportional to the intensity of the incident wave (i.e. proportional to \"E_0^2\") and inversely proportional to the square of the frequency. The classical theory thus leads to the following statements, which are not in agreement with experiment:<\/p>\n\n\n\n\n\n\n\n
Expectation according to the classical theory<\/th>\nExperimental finding<\/th>\n<\/tr>\n
The higher the frequency, the fewer electrons are released.<\/td>\nElectrons are released only above a certain threshold frequency fth<\/sub>.<\/td>\n<\/tr>\n
The energy of the released electrons should decrease as the frequency increases.<\/td>\nThe higher the frequency of the incident light, the higher the energy of the released electrons.<\/td>\n<\/tr>\n
The maximum energy of the released electrons should increase with the intensity.<\/td>\nThe maximum energy of the released electrons does not depend on the intensity at all (only their number does). Below the threshold frequency no electrons are released at all, even if the intensity is greatly increased.<\/td>\n<\/tr>\n
At low intensity the energy is not sufficient to release the electrons. One could argue that the energy “accumulates” over time. One would then expect a time delay before the first electrons are released.<\/td>\nNo time delay before the release of the first electrons can be detected.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Back<\/a><\/p>","protected":false},"excerpt":{"rendered":"

The photoelectric effect shows a number of features that make an explanation in terms of the classical wave theory of light appear difficult. According to the classical theory of the free electron gas, the metal electrons are free particles acted on by the force (where = electric field strength, = angular frequency of the incident… Continue reading What is the problem with using the wave theory of light to explain the photoelectric effect?<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-333","page","type-page","status-publish","hentry","without-featured-image"],"yoast_head":"\nWhat is the problem with using the wave theory of light to explain the photoelectric effect? - milq<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.milq.info\/en\/74-was-spricht-gegen-die-erklaerung-des-photoeffekts-mit-der-wellentheorie-des-lichts\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the problem with using the wave theory of light to explain the photoelectric effect? - milq\" \/>\n<meta property=\"og:description\" content=\"The photoelectric effect shows a number of features that make an explanation in terms of the classical wave theory of light appear difficult. 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