The Photoelectric Effect
"Fifty years of pondering have not brought me any closer to answering the question, what are light quanta?"  Albert Einstein, 1951 ( 1879  1955 )
"... for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"  Nobel Prize Committee, 1921
Nobel Prize Presentation Speech
Excerpts of Presentation Speech by Professor S. Arrhenius, Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences, on December 10, 1922:
Your Majesty, Your Royal Highnesses, Ladies and Gentlemen.
There is probably no physicist living today whose name has become so widely known as that of Albert Einstein. Most discussion centres on his theory of relativity. This pertains essentially to epistemology and has therefore been the subject of lively debate in philosophical circles. It will be no secret that the famous philosopher Bergson in Paris has challenged this theory, while other philosophers have acclaimed it wholeheartedly. The theory in question also has astrophysical implications which are being rigorously examined at the present time.
... Similarly, when a quantum of light falls on a metal plate it can at most yield the whole of its energy to an electron there. A part of this energy is consumed in carrying the electron out into the air, the remainder stays with the electron as kinetic energy. This applies to an electron in the surface layer of the metal. From this can be calculated the positive potential to which the metal can be charged by irradiation. Only if the quantum contains sufficient energy for the electron to perform the work of detaching itself from the metal does the electron move out into the air. Consequently, only light having a frequency greater than a certain limit is capable of inducing a photoelectric effect, however high the intensity of the irradiating light. If this limit is exceeded the effect is proportional to the light intensity at constant frequency. Similar behaviour occurs in the ionisation of gas molecules and the socalled ionisation potential may be calculated, provided that the frequency of the light capable of ionising the gas is known.
Einstein's 1923 Nobel Lecture on Relativity:
English: "Fundamental ideas and problems of the theory of relativity", delivered to an assembly of Nobel dignitaries but not having to do with the Photoelectric Effect for which he earlier received the Nobel Prize in Physics.
German: "Grundgedanken Und Probleme Der Relativitätstheorie"
Einstein's Solution to the Photoelectric Effect
How the metal's surface "Work Function" is determined:
Define:
Derivation:
Equivalent values:
§ Problem 1:
(i). incident light has wavelength 150nm
(ii). cathode element is magnesium with hypothetical "stopping voltage" of 4.620 eV
(iii). what is magnesium's E_{w} ( or φ ), work function?
Solution:
§ Problem 2:
(i). incident light has wavelength 3.5 x 10^{8}m
(ii). cathode element is selenium
(iii). what is the maximum energy of emitted photoelectrons?
Solution:
§ Problem 3:^{∗∗}
(i). incident light has 4,500 Å wavelength
(ii). cathode element has a threshold wavelength of 6,850 Å
(iii). what is the maximum energy of the emitted photoelectrons?
Solution:
^{∗∗}note: this example is used in the future upcoming Relativity Science Calculator Mac application
§ Problem 4:
(i). incident light has wavelength 3.3 x 10^{7}m
(ii). maximum external energy of emitted photoelectrons is 5.6 x 10^{19}J
(iii). what is the metal's E_{w} ( or φ ), work function?
Solution:
§ Problem 4a: what is λ_{0}, the threshold wavelength, for the given metal in Problem 4 above?
Solution:
§ Problem 5:
(i). incident light has frequency 2.5 x 10^{16}hz
(ii). maximum external energy of emitted photoelectrons is 2.9eV
(iii). what is the metal's E_{w} ( or φ ), work function?
Solution:
§ Problem 5a: what is the threshold frequency f_{0} of this metal in Problem 5 above?
Solution:
Photoelectron Work Function, E_{w} ( also: φ ) [ cutoff thresholds: λ^{∗∗∗} = hc / E_{w}, f ^{∗∗∗∗} = c / λ ] 


Cathode Source Element  Symbol  E_{w} in eV^{ [a,b]} ( electron volt ) 
E_{w} in J^{ [d]} ( joule ) 
hc^{ [e]}  λ(meter)  λ( Å) ^{[f]}  freq in Hz ^{[g]} 
Aluminum  Al  4.28  6.86 x 10^{19}  1.99 x 10^{25} Jm  2.901 x 10^{7}  2901  1.0334 x 10^{15} 
Arsenic  As  3.75  6.01 x 10^{19}  ”  3.311 x 10^{7}  3311  0.9054 x 10^{15} 
Barium  Ba  2.70  4.33 x 10^{19}  ”  4.595 x 10^{7}  4595  0.6524 x 10^{15} 
Beryllium  Be  4.98  7.98 x 10^{19}  ”  2.494 x 10^{7}  2494  1.2021 x 10^{15} 
Boron  B  4.45  7.13 x 10^{19}  ”  2.791 x 10^{7}  2791  1.0741 x 10^{15} 
Bismuth  Bi  4.22  6.76 x 10^{19}  ”  2.944 x 10^{7}  2944  1.0183 x 10^{15} 
Cadmium  Cd  4.22  6.76 x 10^{19}  ”  2.944 x 10^{7}  2944  1.0183 x 10^{15} 
Calcium  Ca  2.87  4.60 x 10^{19}  ”  4.326 x 10^{7}  4326  0.6930 x 10^{15} 
Carbonmulti  walled nanotubes  C  4.95 ^{[c]}  7.93 x 10^{19}  ”  2.509 x 10^{7}  2509  1.1949 x 10^{15} 
Carbonsingle  walled nanotubes  C  5.10 ^{[c]}  8.17 x 10^{19}  ”  2.436 x 10^{7}  2436  1.2307 x 10^{15} 
Cesium  Cs  2.14  3.43 x 10^{19}  ”  5.802 x 10^{7}  5802  0.5167 x 10^{15} 
Chromium  Cr  4.50  7.21 x 10^{19}  ”  2.760 x 10^{7}  2760  1.0862 x 10^{15} 
Cobolt  Co  5.00  8.01 x 10^{19}  ”  2.484 x 10^{7}  2484  1.2069 x 10^{15} 
Copper  Cu  4.65  7.45 x 10^{19}  ”  2.671 x 10^{7}  2671  1.1224 x 10^{15} 
Gadolinium  Gd  3.10  4.97 x 10^{19}  ”  4.004 x 10^{7}  4004  0.7487 x 10^{15} 
Gallium  Ga  4.20  6.73 x 10^{19}  ”  2.957 x 10^{7}  2957  1.0138 x 10^{15} 
Gold  Au  5.10  8.17 x 10^{19}  ”  2.436 x 10^{7}  2436  1.2307 x 10^{15} 
Iridium  Ir  5.27  8.44 x 10^{19}  ”  2.358 x 10^{7}  2358  1.2714 x 10^{15} 
Iron  Fe  4.70  7.53 x 10^{19}  ”  2.643 x 10^{7}  2643  1.1343 x 10^{15} 
Lead  Pb  4.25  6.81 x 10^{19}  ”  2.922 x 10^{7}  2922  1.0256 x 10^{15} 
Lithium  Li  2.90  4.65 x 10^{19}  ”  4.280 x 10^{7}  4280  0.7004 x 10^{15} 
Magnesium  Mg  3.66  5.86 x 10^{19}  ”  3.396 x 10^{7}  3396  0.8828 x 10^{15} 
Manganese  Mn  4.10  6.57 x 10^{19}  ”  3.029 x 10^{7}  3029  0.9897 x 10^{15} 
Molybdenum  Mo  4.60  7.37 x 10^{19}  ”  2.700 x 10^{7}  2700  1.1103 x 10^{15} 
Mercury  Hg  4.49  7.19 x 10^{19}  ”  2.768 x 10^{7}  2768  1.0831 x 10^{15} 
Nickel  Ni  5.15  8.25 x 10^{19}  ”  2.412 x 10^{7}  2412  1.2429 x 10^{15} 
Potassium  K  2.30  3.69 x 10^{19}  ”  5.393 x 10^{7}  5393  0.5559 x 10^{15} 
Platinum  Pt  5.65  9.05 x 10^{19}  ”  2.199 x 10^{7}  2199  1.3633 x 10^{15} 
Selenium  Se  5.90  9.45 x 10^{19}  ”  2.106 x 10^{7}  2106  1.4235 x 10^{15} 
Silicon  Si  4.52  7.24 x 10^{19}  ”  2.749 x 10^{7}  2749  1.0906 x 10^{15} 
Strontium  Sr  2.59  4.15 x 10^{19}  ”  4.795 x 10^{7}  4795  0.6252 x 10^{15} 
Silver  Ag  4.26  6.83 x 10^{19}  ”  2.914 x 10^{7}  2914  1.0288 x 10^{15} 
Sodium  Na  2.75  4.41 x 10^{19}  ”  4.512 x 10^{7}  4512  0.6644 x 10^{15} 
Thorium  Th  3.41  5.46 x 10^{19}  ”  3.645 x 10^{7}  3645  0.8225 x 10^{15} 
Titanium  Ti  4.33  6.94 x 10^{19}  ”  2.867 x 10^{7}  2867  1.0457 x 10^{15} 
Uranium  U  3.63  5.82 x 10^{19}  ”  3.419 x 10^{7}  3419  0.8768 x 10^{15} 
Vanadium  V  4.30  6.89 x 10^{19}  ”  2.888 x 10^{7}  2888  1.0381 x 10^{15} 
Zinc  Zn  4.33  6.94 x 10^{19}  ”  2.867 x 10^{7}  2867  1.0457 x 10^{15} 
Zirconium  Zr  4.05  6.49 x 10^{19}  ”  3.066 x 10^{7}  3066  0.9778 x 10^{15} 

Albert Einstein  1921, colorized
Dana Keller: History in Color  http://www.danarkeller.com/
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