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The Photoelectric Effect

"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 photo-electric 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 so-called ionisation potential may be calculated, provided that the frequency of the light capable of ionising the gas is known.


Einstein's Solution to the Photoelectric Effect


How the metal's surface work function is determined:

Einstein's solution to the photoelectric effect

Einstein's solution to the photoelectric effect

Define:

Derivation:

Equivalent values:

Problems

§ 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 Ew ( or φ ), work function?


Solution:

§ Problem 2:

(i). incident light has wavelength 3.5 x 10-8m
(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:

§ Problem 4:

(i). incident light has wavelength 3.3 x 10-7m
(ii). maximum external energy of emitted photoelectrons is 5.6 x 10-19J
(iii). what is the metal's Ew ( or φ ), work function?


Solution:

§ Problem 4a: what is λ0, the threshold wavelength, for the given metal in Problem 4 above?


Solution:

§ Problem 5:

(i). incident light has frequency 2.5 x 1016hz
(ii). maximum external energy of emitted photoelectrons is 2.9eV
(iii). what is the metal's Ew ( or φ ), work function?


Solution:

§ Problem 5a: what is the threshold frequency f0 of this metal in Problem 5 above?


Solution:

Photoelectron Work Function, Ew ( also: φ )∗
[ cutoff thresholds: λ∗∗ = hc / Ew,  f ∗∗∗ = c / λ ]
Cathode Source Element Symbol Ew in eV [a,b]
( electron volt )		 Ew 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 J-m 2.901 x 10-7 2901 1.0334 x 1025
Arsenic As 3.75 6.01 x 10-19 ” 3.311 x 10-7 3311 0.9054 x 1025
Barium Ba 2.70 4.33 x 10-19 ” 4.595 x 10-7 4595 0.6524 x 1025
Beryllium Be 4.98 7.98 x 10-19 ” 2.494 x 10-7 2494 1.2021 x 1025
Boron B 4.45 7.13 x 10-19 ” 2.791 x 10-7 2791 1.0741 x 1025
Bismuth Bi 4.22 6.76 x 10-19 ” 2.944 x 10-7 2944 1.0183 x 1025
Cadmium Cd 4.22 6.76 x 10-19 ” 2.944 x 10-7 2944 1.0183 x 1025
Calcium Ca 2.87 4.60 x 10-19 ” 4.326 x 10-7 4326 0.6930 x 1025
Carbon-multi - walled nanotubes C 4.95 [c] 7.93 x 10-19 ” 2.509 x 10-7 2509 1.1949 x 1025
Carbon-single - walled nanotubes C 5.10 [c] 8.17 x 10-19 ” 2.436 x 10-7 2436 1.2307 x 1025
Cesium Cs 2.14 3.43 x 10-19 ” 5.802 x 10-7 5802 0.5167 x 1025
Chromium Cr 4.50 7.21 x 10-19 ” 2.760 x 10-7 2760 1.0862 x 1025
Cobolt Co 5.00 8.01 x 10-19 ” 2.484 x 10-7 2484 1.2069 x 1025
Copper Cu 4.65 7.45 x 10-19 ” 2.671 x 10-7 2671 1.1224 x 1025
Gadolinium Gd 3.10 4.97 x 10-19 ” 4.004 x 10-7 4004 0.7487 x 1025
Gallium Ga 4.20 6.73 x 10-19 ” 2.957 x 10-7 2957 1.0138 x 1025
Gold Au 5.10 8.17 x 10-19 ” 2.436 x 10-7 2436 1.2307 x 1025
Iridium Ir 5.27 8.44 x 10-19 ” 2.358 x 10-7 2358 1.2714 x 1025
Iron Fe 4.70 7.53 x 10-19 ” 2.643 x 10-7 2643 1.1343 x 1025
Lead Pb 4.25 6.81 x 10-19 ” 2.922 x 10-7 2922 1.0256 x 1025
Lithium Li 2.90 4.65 x 10-19 ” 4.280 x 10-7 4280 0.7004 x 1025
Magnesium Mg 3.66 5.86 x 10-19 ” 3.396 x 10-7 3396 0.8828 x 1025
Manganese Mn 4.10 6.57 x 10-19 ” 3.029 x 10-7 3029 0.9897 x 1025
Molybdenum Mo 4.60 7.37 x 10-19 ” 2.700 x 10-7 2700 1.1103 x 1025
Mercury Hg 4.49 7.19 x 10-19 ” 2.768 x 10-7 2768 1.0831 x 1025
Nickel Ni 5.15 8.25 x 10-19 ” 2.412 x 10-7 2412 1.2429 x 1025
Potassium K 2.30 3.69 x 10-19 ” 5.393 x 10-7 5393 0.5559 x 1025
Platinum Pt 5.65 9.05 x 10-19 ” 2.199 x 10-7 2199 1.3633 x 1025
Selenium Se 5.90 9.45 x 10-19 ” 2.106 x 10-7 2106 1.4235 x 1025
Silicon Si 4.52 7.24 x 10-19 ” 2.749 x 10-7 2749 1.0906 x 1025
Strontium Sr 2.59 4.15 x 10-19 ” 4.795 x 10-7 4795 0.6252 x 1025
Silver Ag 4.26 6.83 x 10-19 ” 2.914 x 10-7 2914 1.0288 x 1025
Sodium Na 2.75 4.41 x 10-19 ” 4.512 x 10-7 4512 0.6644 x 1025
Thorium Th 3.41 5.46 x 10-19 ” 3.645 x 10-7 3645 0.8225 x 1025
Titanium Ti 4.33 6.94 x 10-19 ” 2.867 x 10-7 2867 1.0457 x 1025
Uranium U 3.63 5.82 x 10-19 ” 3.419 x 10-7 3419 0.8768 x 1025
Vanadium V 4.30 6.89 x 10-19 ” 2.888 x 10-7 2888 1.0381 x 1025
Zinc Zn 4.33 6.94 x 10-19 ” 2.867 x 10-7 2867 1.0457 x 1025
Zirconium Zr 4.05 6.49 x 10-19 ” 3.066 x 10-7 3066 0.9778 x 1025
∗ lowest amount of incoming visible light energy in order to release a surface electron where k.e.= 0 - that is, no electron or current flow - and equivalent
to the internal atomic bonding energy unique to each metallic element of electrons to their nuclei.
∗∗ maximum threshold wavelength of incoming visible light in order to release a surface electron where k.e.= 0 - i.e., no electron or current flow
∗∗∗ minimum threshold frequency of incoming visible light in order to release a surface electron where k.e.= 0 - i.e., no electron or current flow
a source: EnvironmentalChemistry.com ( http://environmentalchemistry.com/yogi/periodic/electrical.html )
b 1eV = 1.602 176 487(40) x 10-19 J
c source: Materials Research Society ( http://www.mrs.org/s_mrs/sec_subscribe.asp?CID=2385&DID=137075&action=detail )
d 1J = 6.241 509 65(16) x 1018 eV
e hc = (6.626 x 10-34 Joule - second)(299,792,458 meter/second) = 1.986425 x 10-25Joule - meter ≈ 1.99 x 10-25Joule - meter
f Angstrom = 1x10-10 meter
g 1Hz (hertz) = one frequency cycle per second




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