Relativity Science Calculator - The Photoelectric Effect

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:

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 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.

Einstein's Solution to the Photoelectric Effect

How the metal's surface "Work Function" is determined:

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:

∗∗note: this example is used in the future upcoming Relativity Science Calculator Mac application

§ Problem 4:

(i). incident light has wavelength 3.3 x 10-7m
(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 1015
Arsenic As 3.75 6.01 x 10-19 3.311 x 10-7 3311 0.9054 x 1015
Barium Ba 2.70 4.33 x 10-19 4.595 x 10-7 4595 0.6524 x 1015
Beryllium Be 4.98 7.98 x 10-19 2.494 x 10-7 2494 1.2021 x 1015
Boron B 4.45 7.13 x 10-19 2.791 x 10-7 2791 1.0741 x 1015
Bismuth Bi 4.22 6.76 x 10-19 2.944 x 10-7 2944 1.0183 x 1015
Cadmium Cd 4.22 6.76 x 10-19 2.944 x 10-7 2944 1.0183 x 1015
Calcium Ca 2.87 4.60 x 10-19 4.326 x 10-7 4326 0.6930 x 1015
Carbon-multi - walled nanotubes C 4.95 [c] 7.93 x 10-19 2.509 x 10-7 2509 1.1949 x 1015
Carbon-single - walled nanotubes C 5.10 [c] 8.17 x 10-19 2.436 x 10-7 2436 1.2307 x 1015
Cesium Cs 2.14 3.43 x 10-19 5.802 x 10-7 5802 0.5167 x 1015
Chromium Cr 4.50 7.21 x 10-19 2.760 x 10-7 2760 1.0862 x 1015
Cobolt Co 5.00 8.01 x 10-19 2.484 x 10-7 2484 1.2069 x 1015
Copper Cu 4.65 7.45 x 10-19 2.671 x 10-7 2671 1.1224 x 1015
Gadolinium Gd 3.10 4.97 x 10-19 4.004 x 10-7 4004 0.7487 x 1015
Gallium Ga 4.20 6.73 x 10-19 2.957 x 10-7 2957 1.0138 x 1015
Gold Au 5.10 8.17 x 10-19 2.436 x 10-7 2436 1.2307 x 1015
Iridium Ir 5.27 8.44 x 10-19 2.358 x 10-7 2358 1.2714 x 1015
Iron Fe 4.70 7.53 x 10-19 2.643 x 10-7 2643 1.1343 x 1015
Lead Pb 4.25 6.81 x 10-19 2.922 x 10-7 2922 1.0256 x 1015
Lithium Li 2.90 4.65 x 10-19 4.280 x 10-7 4280 0.7004 x 1015
Magnesium Mg 3.66 5.86 x 10-19 3.396 x 10-7 3396 0.8828 x 1015
Manganese Mn 4.10 6.57 x 10-19 3.029 x 10-7 3029 0.9897 x 1015
Molybdenum Mo 4.60 7.37 x 10-19 2.700 x 10-7 2700 1.1103 x 1015
Mercury Hg 4.49 7.19 x 10-19 2.768 x 10-7 2768 1.0831 x 1015
Nickel Ni 5.15 8.25 x 10-19 2.412 x 10-7 2412 1.2429 x 1015
Potassium K 2.30 3.69 x 10-19 5.393 x 10-7 5393 0.5559 x 1015
Platinum Pt 5.65 9.05 x 10-19 2.199 x 10-7 2199 1.3633 x 1015
Selenium Se 5.90 9.45 x 10-19 2.106 x 10-7 2106 1.4235 x 1015
Silicon Si 4.52 7.24 x 10-19 2.749 x 10-7 2749 1.0906 x 1015
Strontium Sr 2.59 4.15 x 10-19 4.795 x 10-7 4795 0.6252 x 1015
Silver Ag 4.26 6.83 x 10-19 2.914 x 10-7 2914 1.0288 x 1015
Sodium Na 2.75 4.41 x 10-19 4.512 x 10-7 4512 0.6644 x 1015
Thorium Th 3.41 5.46 x 10-19 3.645 x 10-7 3645 0.8225 x 1015
Titanium Ti 4.33 6.94 x 10-19 2.867 x 10-7 2867 1.0457 x 1015
Uranium U 3.63 5.82 x 10-19 3.419 x 10-7 3419 0.8768 x 1015
Vanadium V 4.30 6.89 x 10-19 2.888 x 10-7 2888 1.0381 x 1015
Zinc Zn 4.33 6.94 x 10-19 2.867 x 10-7 2867 1.0457 x 1015
Zirconium Zr 4.05 6.49 x 10-19 3.066 x 10-7 3066 0.9778 x 1015
∗∗∗ 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