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The limiting frequency of the photo-electric effect online

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C 3 17T Obi


Richard Haraer
Ph.D. Thesis






B. A.j University of Saskatchewan 1915

M. A., University of laikatohewan 1918

M. A., TtaiTersity f Trnt 1917

ThBBis submitted in partial fulfillment of the requirenents
fr the degree ef Deoter f Philphy in the Uhireraity ef

Approved ;-

E. P. Lewis
B.E. Hall
W. J. Raymond
T. M. Putnan
II. W. flaskell


_ __ , ^, ^^ L .


;.- -, ' , Introduction.

The discovery by Hertz in 1887, that metals rait negative
electricity when illuminated by ultra-violet light, opened up the new

O *5t

field of photo-eleotricity, he work of Hughes,*" Fdohardson and

o .Ttoii, ; illikan and his co-workers Hannings 7 and Keidesh 6 has pro-


vidod expeririental proof of the Einstein - a ichardson equations as

expressions of the law which governs this effect;

V e = h(0 ->) ) = hO - P = | anr 2

where "V" is tlie voltage required to stop electron emission at the fre-
quency of the incident light "-0" "" ia ^ leiaentary charge, "h" is
Planck's const nt, "P" is the work done ty the electron in escaping from
the parent atomic or molecular system, "m" is the nass and "v" the
velocity of the electron emitted.

1. Hertz, Ann. d. Physik, 31, 421, 98S, 1887.

2. Hughes, Phil. Trans. I.oy. Soo. A. 212, 205, 1913.

3. ichardson, Phil. lag. 23, 615, 1912; Phys. Rev. 34, U6, 1912;

Science 3 , 57, 1912.

4. "ic ardson and Compton, Phil. Mag. 24, 575, 1912.

5. Hillikan, Phys. r ev. 4, 7 , 1914; 55, 1915; 7, 355, 1916.

6. Kadesh, Phys. Rov, !I.S. 3, 367, 1914.

7. Hannings and Kadesh, Phys. R-w. 8, 209, 221, 1916.

8. Einstein, d. Phys. 17, 145, 1905.

- 2 -

As Richardson has said, the parameter of great inportance in
the photo-electric effect has therefore been shown to be the limiting
frequency of the incident light that trill just cause the emission of
electrons with zero velocity or zero kinetic energy.

Than Hv 2 = Vo =

h-J == P That is, the product of ilanck's constant
"h" into the limiting frequency for any elenent affords, as Pohl and
Prin^sheim liave stated, a measure of the work required to be done in
just releasing a bound photo-electron from the parent system. In
view of the recent progress made on ionization potentials for many
of the elements and in thermionic emission, it is of much interest
to learn if there is any relation between the energy required to
ionize the atom, that required to cause "evaporation of electricity"
and that necessary to release electrons by photo-action.

i illikan and Hennings liave developed the above equations,
securing t, e expression] contact difference of potential, C.D.P.=
* ( v ~ v, ) where ""J "and "x|, "are the respective limiting fre-
quencies for t e illuminated surface and the surrounding Faraday
chamber. The energy includes the work required to release the bpund
photo-electron and also that necessary to overcome the contact differ-
enc of potential between the illuminated surface and its enclosing

1. Pohl and Prings eim, Deutsch. Phys. Gcs. Vehr. 15, 637, 1915.


- . >,*.

rfoUBt lO 8 : 31 < :IO.*83Vk-.

ici^*?M>r 1o no V :-?-..


- 3 -

oase. Anderson ar.c T orrison* consider tl at this contact diffrrenoe
of potential between two netals is a measure of the difference in the
energy required to release a bound electron from the molecules of the
two elements respectively.

Precise knowledge, however, of the limiting frequencies for the
various elements ie scarce at present* Results that have so far been
obtained have depended on one of several methods. The usual one has
b en to endeavor to ;easure the maximum energy of emission of photo-
eleotrons from the p rent, systems by means of the retarding voltages
that would prevent the escape of electrons when the surface is exposed
to light of a definite frequency. These values are plotted against the
respective frequencies and, since a linear relationship exists between
then according to the established instein-Riohardson equations above,
the limiting frequency is determined by extrapolation, Richardson and
Compton modified this method by also using the mean energies, which they
considered they could determine more accurately. Contact difference
of potential, surface films and occluded gases make the determination
of the true maximum energy of emission difficult to ascertain exactly,

Anot: er method is to plot saturation photo-currents per unit
intensity of the monochromatic radiation against the wave-lengths and
extrapolate to zero currents. Pohl and I-ringeheim used this, and
Llllikan checked Ids threshold value for lithium, with it. Kopius 1 has
recently depended on it for his value for platinum.

1. .Anderson and Morrison, rMl, I5ag. 25, 24, 1912.

2. Pohl and Pringsheim, Deutsch. Phys. Ges. Verh. 15, 173, 1913.




'I 'I 01



- 4 -


btuhlnann, who worked on silver and platlntci -wedge-shaped

f lias deposited on quartz from incandescent wires, considered the
photo-electric ourroat as a function of both the thickness and the
ave-length. lie plotted the logarithms of the slopes at the origin
of the pho to-current thickness curves against the wave-length and
considers his results those for a metallic layer one molecule thick,
uninfluenced by surface films and occluded gases.

lillikan, Hennings and Kadesh worked mostly on the alkali met-
als with surfac s specially prepared by slaving in vacuo, and they
determined and allowed for the contact difference of potential. Thir
undoubted accuracy was assisted by th fact that their incident light
also included the visible region, giving a greater range of wave-lengths
and allowing their, to secure greater purity of the c-onochroEatic light.
They also obtained much 1 rger photo-currents than one secures from
other elenents.

With the above exceptions, previous deternoinations of the limit-
ing frequencies are not very exact because ti.e contemporaneous contact
difference of potential was in wany oasos not determined and allowed for,
or that the wrong slope of the energy-frequency curve was used, due to
erron.oous values of the retarding potentials being secured because of
tho effects of scattered light, as in the case of Hughes 1 work, and stray
diffuse light of higher frequencies than the selected ones, as in the
investigations of Richardson and Compton. Therefore the esti:aated

1. Kopius, Phys. -^ev., 18, 443, 1921.

2. Stuhliaann, ,hys. 'ev., 15, 549, 1920.

;: J.: .:- jcir , ... ' ... wri^

. - . -



,-.-: %>iddBNNR- fcaoftawltfc -...

PT f - ; :r- i-c

- 5 -

threshold values given by Hughes for Ca, Jig, Zn, Pb, Bi, Sb, As and
Se and those by "ichardson an Corapton on Na, Al, Kg, Zn, Sn, Bi, Cu,
and Ft are only true within a range of accuracy of several hundred

T.troEi unite. In fact the differences between the values given by
the above are 520 an; stroris for : ',;;, 744 for Al and 67 for ^i hven
Millikan in his photo-electric deter' ination of the most accurate
value of Planck's constant "h", after checking his results on lithium
and sodium b; both methods, did not claim an accuracy greater than
100 angstroms.

fhe contact difference of potential between the case and the
exposed aetal varies, as is shown by the work of Page 1 , Hennings ,

*^ A. I ^

Kadesh , lailikan , and .jvdcrson andtorrison , due probably, as Itilli-
kan ^onoludos, to the variations in the formation of surface films on

all the metallic surfaces. Fiersol showed by heating strips that the
photo-electric current varied with the evolution of gas and that a
greater effect succeeded, together with the disappears oe of all ab-
normal effects. he surrounding gas has been shown by Fredenhagen ,
Paech , iv'iedemann and Hallwachs to be of considerable iiqportance.

1. Page, Araer. Gl. Science, 36, 501, 1913.

2. Jennings, loo. cit.

3. Kndeah, loo. cit.

4. ' illikan, loc. cit.

5. Anderson and Ivlorrison, loo. cit.

6. Pierson, Phys. Rey. 7, 238, 1916.

7. Fredenhagen, Phy. Zeit. 15, 65, 1914.
3. Paech, Ann. d. Phys. 43, 135, 1913.

9. Wiederaann and Hallwaohs, Deutsch. Phy. '^es. Verh. 16, 107, 1914.


- 6 .

liennings and Kadeah observed a falling off of the maximum energy of
emission with increasing age of surface. Photo-electrio "fatigue"
or the diminishing of the photo-eleotric current with the time of
photo-action is a matter of common experience in this work

The difficulties of experiments in this field, namely the ef-
fects of scattered light, reflected light, and reflected electrons,
surface filns and occluded gases, and contact difference of potential,
vitiate seriously the accuracy of determinations of the limiting fre-
quency by the riethod of estimating from the positive potentials acquired
by the exposed surface using the linear relationship that exists between
energy and frequency.

The other method of determining the saturation photo-currents
per unit intensity of the incident light is free from some of these
difficulties, but still demands great purity of the monochromatic light,
and also an accurate contemporaneous determination of its intensity,
nhioh experimentally reduces the currents obtained making the deter-
mination of the "end" point less easy to ascertain.


- 7 -


This research was undertaken with a viev? to determining directly
and if possi la more precisely than hitherto the limiting frequencies
for the various elementary metals under ordinary conditions* The prin-
ciple of the method adopted was to use a source giving an approximately
continuous spectrum extending over the experimental range of the limit-
ing frequency for an element and to determine the threshold v lue by

plotting the last final valu-s of the diminishing saturation photo -

currents against the increasing wave-length of the incident light, or

simply to take the average of the close v;ave-length limits observed.

This direct method of a source giving a continuous spectrum and
the measurement of the saturation current undoubtedly possesses many
advantages over most previous methods. Cell construction is not so
important, since the reflection of light or reflection of electrons,
stray magnetic fields or contact differences of potential oun not affect
the values of the saturation currents, lloreover, a knowledge of the
relative intensities of the radiation at different wave-lengths is not

Ho special preparation of the metallic surfaces WPG made as did
rfennings, Kadesh, and 11 likan save that of rubbing with sandpaper ,
blowing with dry air, and evacuating the photo-electric cell imnediately
to a gas pressure of about 0.006 inn 1 ., of mercury.




dktfT S-* 5

vJllsJsv attt '..:. risW/*n . . ; ^.,o4cs 0*

** 'to - .. '


- 8 -

Tlie apparatus was Designed to cause as little absorption of the
ultra-violet light as possible. It consisted of a modified LittrWi
type of spectroscope used with a concave mirror in the place of lenses.
The light from the source entered the slit at s and was directed
onto the face of the fluorite prism P by the concave mirror b, formed
by oathodio spluttering of platinum on a glass concave lens. The
prisia was mounted in the box x so that the center of the face nearest
the concave mirror was on the rigidly fixed axis of rotation of the
whole box x, *' ose movement was controlled by a double tangent screw
motion shown, in part, at t. A projecting rod A rigidly attached to the
small cencral table supporting the prism carried a guide g_ to which piv-
oted two arms n and m, one fastened to the box carrying the slit s and
mirror b^ by ;eans of a pivot at a post d, t e other pivoted to the spec-
trometer arm 1. Thus once a setting of o was made on a line for maximum
deviation, rotation of the tangent screw caused other lines to appear,
which in turn traversed the ; riao. at minimum deviation. Since a mir-
ror was used in ple.ce of lenses, the focusing of one line on the slit
o was sufficient for all. In use, it was found best to fix the spec-
trometer arm 1 rigidly to the table and move the whole box with slit
and mirror by rotating the tangent screw. This necessitated attaching
the source of light firmly to the box, which was managed by one or
other of the two attached arms e and f. The rotation of the prism
was observed and measured very accurately for the purpose by the re-
flection of a straight filanent L as source from a plane-concave cylin-
drical glass lens II, whose concave surface had been covered with a
platinur, film by cathodic spluttering, placed abov on the axis of



sir '. - -/filar vso'-'Vii **."-"

H-ta e

^.. r,< - , ' . '




Spectrometer scale


Figure 1 .

; v i r ..

:; I" 9'

- 9 -

rotation. This gave an excellent line image on a ruled meter scale
153 c .s. a\;ay visible even in daylight.

In spite of a considerable b cklash, a setting could be
made to a fifth of a nillineter, which corresponded to an angle of
0.45 minutes of arc, i.e. ubout 30 seconds.

The photo-electric cell C consisted of a brass tube closed at
one end by a slit about 0.7 mm. wide at cs and at the other end by the
quartz window Q. The fluorite window F allowed the light of the de-
sired wave-length from the prism to be focused sharply t c inside
the exhausted glass tube V. To assist in correct focusing, the slit
end o of the oell was coated with luminous zinc sulphide. The whole
tube V could be rotated around a ground glass joint with a mercury
s al placed below it on the exhaust tube.

The netal to be tested was in the form of a flat strip about
4 x 18 mm. suspended from a brass rod sealed in glass with sealing
wax passing through a mercury sealed ground glass joint above.

An area about 4 x 10 mm. was exposed to the radiation by pro-
jecting through the top of the brass photo-electric oell. By ro-
tating thJs strip edgewise and by the use of a lens at Q, or by sus-
pending a fluorescent screen in place of the metal strip, it was
possible to set very exactly on some known line of the Hg arc spectrum.

The metallic strip was connected by the brass rod to a string
electrometer with a sensitivity from 50 to 100 divisions per volt but
a cap- city of only about 25 cm. (C.G.S. units). This is represented
diagramatically at H. One knife edge was charged positively to 75
volts, the other negatively to the, with respect to the earth.


.* no *1 M

MBJ^W^ rf OJ J

'c. a

- 10 -

The capacity was kept as low as possible by having the electroneter
close, and, of course, it was necessary to shield everything from
eleo-roetx tic interferences. The F raday chamber was connected to the
knife edge positively charged. T he cell was about 8 cos. in length
in a glass tube abo;t 12 ona. lori and its diameter was about 2.5 cms.
he si t of t a cell was about 41.5 cms. from 0, the axis of rotation,
which -.s ii; cms. from the rdrror, which in turn was 31 cms. from the
slit. ;;;e ultraviolet light, therefore, had to travel about 84.5 cms.
in air after passing through the sl't.

Owing to the considerable amount of scattered light of all
frequencies, it was desirable, in some oases, to use filters to ex-
tinguish, as far as possible, the diffuse light of higher frequency
than the selected oue. Only filters for the short wave-length side
were necessary. Different thicknesses of oalcite and glass were
generally used, i'a.croscopic cover glasses of various thicknesses
were extremely useful. In the case of platinum it was found necess-
ary to blow large bubbles of glass and select several thin pieces
for trial.

- 11 -



On first setting up the photo-electric cell, it was necessary to
bo sure that the line on the slit e was due to the ..ave-length at minimum
deviation, so that the dispersion curve for fluorite oould be used in the
identification of the lines. Therefore a reading microscope sliding in
a long tube supported along the arm 1, but directed towards the middle
line of the nearest face of the prism, was used to set on the sodium D
lines and the visible mercury lines. Corresponding prism angles were noted.
' he tube and microscope were now removed because the tube reflected light
internally and the photo-eloctric cell was then arranged to catch the par-
ticular wave-lengths at the same prism angles as denoted by the scale.

The lines were next visually identified by means of a zinc sul -
phide screen and comparison with spectrograms of the mercury arc spectrum.
However, in order to nake absolutely certain of the effective location of
monochromatic radiation on the metallic strip, a series of observations
of the photo-electric current were taken for each metal at every 2 mm. of
the scale, namely "t about every 4.5 minutes of arc. This enabled an ac-
curate calibration to be made and safeguarded against accidental displace-
ment of the cell while a transfer of elements was taking place, besides
assisting in giving a rough determination of the threshold value.

With this experimental arrangement a series of measurements of the
relative photo-electric currents at different wave-lengths was made. If
there were no effects due to scattered light snd if the slit were infi -
nitely narrow, the current would begin to rise rapidly at the critical
wave-length. The effect of both of these is to make a rounded, instead of
a sharp, break in the current-wave-length curve. By the use of thin
filters the effect of shorter scattered wave-lengths was reduced.



a oft? no J"B o

ervsl -vi ^> v

btsti *'.':..+ =*::

"j 'I

- ItfB ar.-ts '":c ^.-.^-r- -^..f
Jta "i'*.~

lo ^cr-teoof eTih*tt er
ar sf' i" 1 !**

lo .ca: S -n^ ^ ' iJ*te*


-:> -iz.:*- r,= *f.:j.-ooj s.

K'sziz-jJ ^.- -.:.'..- .n.:r5t-.* a J'.jv .-..' lo -je'tsfuri^ A IJbiw HCD

,e?iJjv blosteeirf^ art* lo fto 1 * :n.ri?rt3.Jfc agucit a gnlrlj ai 31


.'^ J:

he slit was C#7 ram. wide, covering a range of from 36 to 100 angstroras,
approximately. It is assumed that the two points of rapid inflection in
the curve (Figure 2) indicate the points at which the critical wave -
length be -an and ceased to fall upon the slit, and the effective wave -
length urns tahen as lying "between these two points. The aver ge was
taken, generally.

The line A 2536 of the mercury arc v; s used as a point of refer-
once, and the critical wave-lengths determined in terras of distance from
this point, with the help of the calibration curve.

- 13 -

Observat ens and results

Zinc: The results of fourteen series of obsarvat:' ons are given
belov;, in scale readings with reference to A253o and In wave-lengths, '
some without and some with a thin glass filter; and with the mercury arc,
the solid carbon arc, and the soaked oarbon arc. rbons with soft cores
were soakod in a concentrated solution of iron, nickel and uranium sulphates,

Mercury Arc Solid Carbon xiro.

Glass filter Ho filter lassTTlter.

47T A3406 TI A3520 4.r~ A 3442 4.c * 344"F~

4.0 3380 4.4 3520 4.05 3393 3.G 3Li51

3.8 331G 3.85 3332

3.8 3316 3418 3347

3.8 3310 3457

3.6 3251 Soaked Carbon Arc

No filter

3331 4.2 A 3442

m Final Average, A 3382.

The solid or rbons probably give more accur te results since they
would not be so likely to produce much ultra-violet light below the
threshold value for xino and so ..Ake the use of filters less necessary.
Thus larger photo-currents were secured and hence more reliance was
placed on these.

In more detail, they re as follows, the readings indicating the
limits between which the curve changed its gradient:

Solid Carbon Aro.
No filter Thick glass filter

4.0 to 4.T~or * 3380 to 3406 4.1 to 413 or A 3406 to 3480.

4.1 to 4.3 or 3406 to 3480.

he average of these three is 3426 angstroms ranging fromX33G5
to ^ 3599 if we consider 2 ran. as the experinental error due to width of
slit, impurity of spectrum, uncertainty of exact end point, due to the
readin-s being of long durat'on usually, and the effect of iero drift.
It would appe r tlv.t the limiting value for zinc could have been

; " 3

- ...

- 14 -

obtained directly with the carbon arc, but ^roater confidence WGB placed
in the results when they were tested with filters that absorbed much of
the shorter wave-length radiation.

The threshold val^e for zinc was, therefore, taken to be A 3426 - 75.

Silver; '"he separate observations on silver, all taken with the
carbon ars, pre summarized es follows:

Cored carbons (.'ore-soaked carbons h^o 1 i d carbons

Ho filter" "iTTass filter .o filter" "lass filler r lass filter

3406 - 3Sfe5 ""334T - 3315 34T2~ 5348 3542 - 3365 15*95 - 3348
3442 - 3365 3406 - 3391 3406 - 3390

340G - 3365

The averages of all the above give the value "A 3391, while the

' - *

extremes give, b;- averaging also, a range fron "A 3421 to A 3361. Thus
the observed threshold value for silfer is A 3331 - 60.

Flatinura: The ^observations on corcimsriially pure platinum with
the carbon arc, soft cored but not soaked, are surani, rized below:

J12. filter Thin glass filter Double glass f i Iter
800~^ 2T53 2805 - 2747 ?800 2762

2782 - 2713 2782 - 2713

2901 - 2753

averages of all the above give "A 2782 while the extremes
give an average range from A 2811 to "A 2740, The observed critical


wave-length for platinum was therefore, A 2782 - 35.

Aluminum; The readings observed on aluminun with the carbon
arc (soft cored but not soaked) using a glass filter are as follows:

A 3142 3285 33)5 3442 3542 3585 3649 3747
1.0719 .0358 .0193 .0114 .0073 ,0057 .0-057 .0048

These readings of current and v/ave-length are plotted in the typical

curve, '.,. Z. The threshold value for aluminum is about * 3596 * 100.



















Limiting Wavelength For Aluminum.
Carbon are (cored)
Glass filter.


3200 3400 3 b

Wavelengths in Angstrom Units.

Figure 2.


- 15 -

Sui::: -ary o e suite and Comparisons .

1 2

Ifetrier ^ Herman B Bwmingi St\jhl- Kopius Hughes Idohardson Lenard

and raann. and and


Zn S42C 75 3132 - 3342 3342 3016 37SO 2600

Ag 3591 60 3650 3250

Ft 8782 35 2840 2570 2880 2600

Al 3596 i 100

1. Gtuhlnann, Itiys. Pev. br. tract, 1920.

2. Lenard, Ann. d. Phys., 8, 149-198, 1902.

3. Ladenburg, Verb. d. Deutsc;, 3hys. Gee. IX, 504, 1907,

- 16 -

Comparison o Re suit s_.
Incorrect values of the constants, as was indicated above,

made Hughes' values too low and Richardson and Compton's too high.
Jennings used the Hilger monochromatic illuminator, which causes con-
siderable absorption and makes the photo-currents near the critical
wave-length very difficult to detect. His higher limit for sine is
prao-.ically within the limit of error so that the agreement is fairly

For silver, Btuhlmann gave A 3250, which is lower than observed
here. The purity of the specimens used nay account for this or th
conditions of his experiment as regards occluded gases. It must be re-
marked, also, that he only made one determination at aoh thickness, so
that equilibrium, as regards photo-electric action, nay not have been
s cured as it probably was in these experiments where the surface was
flooded with ultra-violet light, oonnencing on the short wave-length
side of A 2536.

Kopius states that he used pure platinum. Presumably this was
oli mic lly pure, whereas these results are for eorar-eroially pure. Then
again, his treatment was such as to drive to the surface influential
occluded gases. There is also a possible criticism, too, of the method
used by him of supposedly plotting photo-currents per unit intensity of
the monochromatic radiation* These lines have a definite range of action
for the cell in position, due to the finite width of the slit, and strong
lines will also have a different effective width. It is probably not cor-
rect to simply tak the observed photo-current at the central -osition of
this range. The whole integrated effect of each line should be used. This
neglect probably changes the slope considerably and leads -o an incorrect


Online LibraryRichard HamerThe limiting frequency of the photo-electric effect → online text (page 1 of 2)