Einstein's famous explanation of the photoelectric effect is addressed using the Minkowski four-vector formalism. This formalism deals with energy and linear momentum simultaneously and it is Lorentz covariant. The energy and momentum equations for both electron emission and electron braking are obtained in the lab frame S. It is then shown that the energy and momentum equations for electron emission and electron braking in a second inertial frame are linear combinations of the corresponding equations in the original frame S, according to the principle of relativity. Although the photoelectric effect is basically a non-relativistic phenomenon, the approach presented here may provide new insights for both instructors and students.
References
1.
R.
Wolfson
, Essential University Physics, Vol. 2
, 2nd ed. (Addison-Wesley
, San Francisco
, 2012
), pp. 612
–614
.2.
R. A.
Powell
, “Photoelectric effect: Back to basics
,” Am. J. Phys.
46
, 1046
–1051
(1978
).3.
H. D.
Young
, R. A.
Freedman
, and A. L.
Ford
, Sears and Zemansky's University Physics with Modern Physics
, 13th ed. (Wiley
, San Francisco
, 2012
), pp. 1261
–1265
.4.
R. N.
Steinberg
, G. E.
Oberem
, and L. C.
McDermott
, “Development of a computer-based tutorial on the photoelectric effect
,” Am. J. Phys.
64
, 1370
–1379
(1996
).5.
Mervi A.
Asikainen
and Pekka E.
Hirvonen
, “A study of pre- and inservice teachers' understanding of photoelectric phenomenon as part of the development of a research-based quantum physics course
,” Am. J. Phys.
77
, 658
–666
(2009
).6.
T. R.
Carver
and J. O.
Crawford
, “Useful lecture demonstration of photoelectric wavelength threshold
,” Am. J. Phys.
43
, 370
–371
(1975
).7.
A.
Cortel
, “Simple photoelectric effect
,” Phys. Teach.
44
, 310
–311
(2006
).8.
R. J.
Hanson
and B. E.
Clotfelter
, “Evaluation of commercial apparatus for measuring h/e
,” Am. J. Phys.
34
, 75
–78
(1966
).9.
A. W.
Knudsen
, “A photoelectric determination of h/e: A new approach to an old problem
,” Am. J. Phys.
51
, 725
–729
(1983
).10.
A.
Ahlgren
, “Apparatus for teaching physics: Inexpensive apparatus for studying the photoelectric effect and measuring Planck's constant
,” Phys. Teach.
1
, 183
–186
(1963
).11.
J.
Walker
, Halladay and Resnick Principles of Physics. International Student Version
, 9th ed. (Wiley
, Hoboken
, 2011
), pp. 1059
–1064
.12.
H. H.
Hall
and R. P.
Tuttle
, “Photoelectric effect and Planck's constant in the introductory laboratory
,” Am. J. Phys.
39
, 50
–54
(1971
).13.
R. A.
Serway
and J. W.
Jewett
, Jr., Principles of Physics. A calculus-Based Text
, 3rd Ed. (Harcourt College Publishers
, Orlando
, 2002
), pp. 1049
–1056
.14.
M.
Iona
, “Stopping potential for photoelectrons
,” Am. J. Phys.
34
, 707
(1966
).15.
P.
Gluck
and B.
Saering
, “No time lag in the photoelectric effect
,” Phys. Teach.
48
, 285
–286
(2010
).16.
H. D.
Young
, R. A.
Freedman
, and A. L.
Ford
, Sears and Zemansky's University Physics with Modern Physics
, 13th ed. (Wiley
, San Francisco
, 2012
), p. 1263
.18.
J.
Rudnick
and D. S.
Tannhauser
, “Concerning a widespread error in the description of the photoelectric effect
,” Am. J. Phys.
44
, 796
–798
(1976
).19.
H. D.
Young
, R. A.
Freedman
, and A. L.
Ford
, Sears and Zemansky's University Physics with Modern Physics
, 13th ed. (Wiley
, San Francisco
, 2012
), p. 1264
.20.
A. B.
Arons
and M. B.
Peppard
, “Einstein's proposal of the photon concept–a translation of the Annalen del Physics paper of 1905
,” Am. J. Phys.
33
, 367
–374
(1965
).21.
R.
Kidd
, J.
Ardini
, and A.
Anton
, “Evolution of the modern photon
,” Am. J. Phys.
57
, 27
–35
(1989
).22.
R. A.
Millikan
, “A direct photoelectric determination of Planck's ‘h’
,” Phys. Rev.
7
, 355
–388
(1916
).23.
D. R.
Lloyd
, “What was measured in Millikan's study of the photoelectric effect?
,” Am. J. Phys.
83
, 765
–772
(2015
).24.
R.
Baierlein
, Newton to Einstein: The Trail of Light
(Cambridge U.P.
, New York
, 2002
), pp. 151
–154
.25.
G.
Margaritondo
, “A historically correct didactic first step in the quantum world: stressing the interplay of relativity, thermodynamics and quantum physics
,” Eur. J. Phys.
24
, 15
–19
(2003
).26.
R.
Chabay
and B.
Sherwood
, Matter and Interactions. I. Modern Mechanics
(Wiley
, New York
, 2002
). pp. 1054
–1057
.27.
H.
Hall
and J. R.
Oppenheimer
, “Relativistic theory of the photoelectric effect
,” Phys. Rev.
38
, 57
–79
(1931
).28.
H.
Hall
, “On the relativistic photoelectric effect
,” Phys. Rev.
45
, 216
–217
(1934
).29.
J.
Güémez
, “An undergraduate exercise in the first law of relativistic thermodynamics
,” Eur. J. Phys.
31
, 1209
–1232
(2010
).30.
J.
Freund
, Special Relativity for Beginners
(World Scientific
, Singapore
, 2008
), Chap. 34.31.
J.
Güémez
, M.
Fiolhais
, and L. A.
Fernández
, “Relativistic mechanical-thermodynamical formalism—Description of inelastic collisions
,” Eur. J. Phys.
37
, 015602
(2016
).© 2018 American Association of Physics Teachers.
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