G. N. RAMACHANDRAN AND S. RAMASESHAN

(a) for the incident azimuth a= 00 or 900

2Vo= 2p(1-6 2 /6) 7 , (16a)

and (b) for a= 450,

21/45= 2 p(1+6 2 / 3 ). (16b)

The error in using these approximate formulas is lessthan 1 percent so long as and 2p do not exceed 300.

tan2p=

It will be noticed from the forementioned formulasthat the apparent rotation is less than the true rotationwhen cz=0 or 900, but is more when a= 4 50 . It isinteresting to see what would be the average value of2iP for all azimuths a of the incident light. Thus, fromEq. (12), tan2ib has the value given below for a par-ticular value of 2a:

sinm2y sinA- (1- cosA) cos22,y tan2a+ sin2y sinA tanm2 a

cos22'y+sin2 2y cosA+cosA tan2 2a

The mean value of tan2if over the range - 7r/2 to+7r/2 of 2a can be shown to be the remarkably simpleexpression

(tan2V/')m= [cotA(cotA+ cosecA cot22y)]A. (17)

With the same approximations as were used in derivingEqs. (16a) and (16b), one obtains

2 iPm=2 p(1+ 2 /12 ). (18)

Although the deviation in the mean value of the appar-ent rotation is less than the deviation for either a =0or a=450 , it does not vanish.

However, Eqs. (16a) and (16b) suggest a simplemethod of eliminating the effect of birefringence, withoutmeasuring its value. We have, from these,

(260o+14)/3=p, P(19)and this equation is correct to the third order in 6, theonly terms that occur being &4 and higher powers.

The above formulas can be verified to be true fromthe data in Table I. The entries in the second row corre-spond to 6=32.40, which is near the limit of validity ofthe formulas. It is seen that the decrease in ip for a =0is nearly half the increase for a= 450 and their magni-tudes are what are given by Eqs. (16a) and (16b).Further (2ito+,64s)/3 is 17.35°, which differs from thecorrect value 17.40 by less than 0.5 percent.

Another approximate formula, valid when 2p is small(<30°) and > 2 p is

2iA = 2 p sin6/6, (20)

if a =0. For a= 450 26 increases indefinitely with in-crease of 8. The relation between the two is

tan2ifr=2p tan6/6, (21)

but this is not a convenient equation to use.Equations (16) and (20) cover practically the whole

range of values which occurs in Faraday effect studies,and can be used to deduce the true rotation from themeasured apparent rotation.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 42, NUMBER 1 JANUARY, 1952

Energy Levels and Wavelengths of the Isotopes of Mercury-198 and -202

KEIVIN BuRNs, Allegheny Observatory, Pittsburgh 14, Pennsylvania

AND

KENNETH B. ADAMS, Westinghouse Research Laboratories, East Pittsburgh, Pennsylvania(Received September 10, 1951)

In the region 6709-2302A the wavelengths of sixty lines in the first spectra of the even isotopes of mercury,sHg10 3 and soHg2 , have been measured relative to 5460.7532A. Electrodeless tubes (see reference 3) contain-ing 0.5 mg of mercury were excited by radio waves of 90- to 300-mc frequency. Comparison with the dataof Meggers and Kessler (see reference 5) shows the median difference AOW-MK to be 0.0001A. A compari-son of the wavelength and level systems of the two isotopes confirms our opinion that the spectrum ofnatural mercury may be useful as a source of secondary standards, since the isotope shift of the odd level6p PI' is nearly the same as that of several even levels.

We are indebted to Director Condon and Dr. Meggers of the National Bureau of Standards for a sampleof 80Hg'98 which was derived from radioactive gold in cooperation with the United States Atomic EnergyCommission. The sample of soHg20l was produced by Carbide and Carbon Chemical Division, Oak RidgeNational Laboratory, Y-12 Area and obtained on allocation from the Isotopes Division of the AEC.

IN continuation of the search for secondary standardsof wavelength the spectra of mercury 198 and 202

have been observed throughout the region 6709-2262A.

The method of observation was the same as that usedto observe the spectra of neon and mercury' with the

I Burns, Adams, and Longwell, J. Opt. Soc. Am. 40, 339 (1950).

56 Vol. 42

MERCURY ISOTOPES 198 AND 202 SPECTRA

TABLE I. Wavelengths in the spectra of mercury 198 and 202.

1 2 3 4 5 6 7soHg'

9 8

Vacuum Wave Number No. LevelX in air observed computed X MK obs. combinations X in air

6907.46126716.42896234.40206072.71285790.66265789.669C5769.59845675.92255460.75325354.029-4916.06814358.33724347.49584339.22444108.05744077.83794046.57123906.37153903.639C3901.86683801.66013704.16983702.353C3701.43223663.28083662.88263654.83923650.15643341.48143131.84233131.55133125.66983027.48963025.60803023.47643021.49962967.28322925.41352893.59822856.93892806.765-2805.347-2804.43782803.47062759.71032752.78282699.862C2699.378-2698.83142674.917-2655.13052653.68272652.04252639.790-2576.29042563.86102536.50632534.76912483.82152482.71312481.99932464.06362446.89982400.497-2399.72932399.34852380.00402378.32462345.44002302.0651

14473.11414884.76316035.60416462.55717264.40617267.-17327.43517613.40618307.41818672.34420335.79822938.10622995.30523039.13824335.56324515.90324705.32625591.98225609.-25621.52626296.85926988.95227002.-27008.91327290.19027293.15727353.22027388.31129918.27531920.86731923.83331983.90033021.08133041.61733064.90833086.54133691.05134173.22734548.94734992.23925617.73335635.74-35647.29135659.58636225.00536316.16037027.-37034.60237042.10637373.24937651.74337672.28537695.58037870.53738803.89038991.99339412.46739439.47440248.39320266.36040277.93640571.09640855.65341645.35141658.67441665.28542003.90442033.56542622.85143425.862

Pa4.7625.6072.559D7.3707.4393.404ppSpDDSSpD9.892DSD2.1978.9-0.1793.1443.213D8.2620.8673.8323.9011.0791.5974.912D1.0523.2088.9502.2607.7565.6667.300D4.9786.1707.9714.64-D3.2311.7672.2855.600D3.8962.024S9.5058.4446.3547.9881.1165.6665.4148.6595.32-3.9193.5742.8865.879

0.6626

9.5984

0.7532

8.33767.4957

7.83796.5715

3.2808

0.15671.48141.84201.55105.67007.4896

3.47621.49977.28335.41323.5980

3.4699

2.7827

5. 13003.68262.0426

6.5064

8 7s S - 8p 3P 2 '5 7s So - 8p P5

0

5 - 7s 'So - 9p 'P,'3 7s S - 8p Pi0

46 6P iPs0_ 6d 'D2C 6p Pi 0- 6d 3Di

50 6p 'Pi- 6d 3D28 7s 3S, - 9p 5P5

0

80 6p 3 P20- 7s 3S,

2 7s 3S -lOp 3P20

28 6p 'Pi,- 8s So104 6p 3p,°- 7s S,43 6p P 5

0- 7d D232 6p spilo_ 7d 3D214 6p sP1-. 9s 'So82 6p 3P,'- 7s 'So96 6p 3Po°- 7s 3Ss18 6p lP 0- 8d 1D2C 6p 'Pi 0- 8d 3D1,11 6p Pl°- 8d 3D2.10 6p 'P, 0-10s iSs12 6p 'Ps 0- 9d 1D2C 6p P,°- 9d D,4 6p 'P,°- 9d 3D2

35 6p 3P2°- 6d 'D27 6p 3P2°- 6d 3D,

85 6p 3P2°- 6d D,85 6p 3P2,- 6d 3D374 6p 3P2°- 8s Ss28 6p 3P1°- 6d 'D225 6p 3P?0- 6d 3Di81 6p 'P 1

0- 6d 3D214 6p 3P20- 7d 1D26 6p 3P?0- 7d D,

23 6p 3P2 o- 7d 3D234 6p 3P2

0- 7d 3D337 6p 3PO°- 6d D17 6p 3P20 - 9s 3S130 6p 3P1

0- 8s 3S,8 6p 3P5

0- 8s So2 6p 3P2

0 - 8d 1D23 6p 3P?0- 8d 3D1

11 6p 3P, 0- 8d 3D221 6p 3P°- 8d 3D34 6p 3P2

0-lOs 3S,23 6p 3PO°- 8s S,C 6p P?0 - 9d 3Di1 6p 3Po- 9d 3D29 6p 3P20- 9d 3D32 6p P2-11s 'S,

22 6p 3P,0 -- 7d 'D222 6p 3P5

0- 7d D,26 6p 3P5

0- 7d 3D21 6p 3P20 -10d 3D3

33 6p 3P,0- 9s 3S,4 6p 3P,'- 9s 'So

55 6s2 'So - 6p 3P,138 6p 3PO°- 7d 3D123 6p 3Pl0 - 8d D231 6p 3P,0 - 8d 3D,42 6p 3P?0 - 8d 3D220 6p 3PO°- 9s Ss18 6p 3P'-10s 'S,3 6p 3PO.- 9d 'D28 6p 3P,0.°- 9d 1,

15 6p 3Np1-- 9d 3D25 6p 3P 0 -lls 'Si

23 6p 3Po°.- 8d I6 6p 'Ps 0-lOs 356 6p 3Po°- 9d 3Di

6907.46756716.32536234.37766072.62605790.66485789.671C5769.60005675:90425460.73555354.044-4916.06774358.32574347.49674339.22514108.05724077.82844046.56193906.37153903.638C3901.86623801.66193704.17123702.351C3701.436-3663.27783662.88013654.83613650.15323341.47663131.83943131.54803125.66753027.48743025.60563023.47393021.49732967.28192925.41042893.59522856.93572806.76302805.34742804.43572803.46782759.70772752.78012699.858C2699.375-2698.82932674.914-2655.12842653.68092652.03992639.784-2576.28822563.85842536.52772534.76622483.81962482.71122481.99712464.06142446.89742400.49592399.72712399.34622380.00202378.32242345.43692302.0620

8 98oHg2G2

Vacuum Wave Numberobserved computed

14473.100 Pa14884.992 4.99516035.666 5.66716462.792 2.79017264.399 D17267.- 7.36217327.430 7.43217613.463 3.46218307.477 P18672.293 P20335.800 S22938.166 P22995.300 D23039.134 D24335.564 S24515.960 S24705.383 P25591.980 D25609.- 9.89725621.530 D26296.847 S26988.942 D27002.- 2.21227008.884 8.88-27290.213 0.20727293.176 3.16827353.243 3.23827388.355 D29918.318 8.29831920.896 0.89631923.866 3.85731983.923 3.92733021.105 1.10633041.643 1.62533064.936 4.94033086.566 D33691.066 1.07434173.263 3.24134548.983 8.98734992.279 2.29535617.760 7.78635635.733 5.70335647.318 7.33635659.621 D36225.039 5.01636316.195 6.20437027.- 8.02837034.643 4.64537042.132 D37373.298 3.26537651.772 1.79537672.310 2.31437695.617 5.62937870.615 D38803.923 3.93038992.032 2.05939412.134 S39459.519 9.53140248.422 8.47540266.391 6.39240277.972 8.02540571.132 1.14740855.693 5.70541645.370 5.43741658.712 8.70741665.327 5.33442003.939 3.95442033.603 3.60942622.908 2.92243425.920 5.924

* A letter in column 3 indicates that this is the only line used to evaluate one of the levels involved, here 8p 3P2'.

January 1952 57

10

No.obs.

10575

38C

394

5339

5325176

505511C867C2

173

575054262856139

16182115199539

155

15C1

111

1616162

144

20137

1014102078

176

2089

-

K . BURNS AND K. B. ADAMS

TABLE I.-Continued.

1 2 3 4 5 6 7 8 9 10isI-g' ssHg2S

Vacuum Wave Number No: Level Vacuum Wave Number No.X in air observed computed X MK obs. combinations X in air observed computed obs.

3983.8394 25094.343 ... ... 12 3983.9941 25093.368 ... 122916.2269 34280.875 .. *-... 5 2916.2645 34280.433 *.. 42847.6752 35106.072 ... 8 2847.6716 35106.116 ... 62262.2097 44190.859 ... 25 2262.2306 44190.451 ... 21

NOTES TO TABLE 1.3702A and 2699.8A. These lines are included because, though not seen,

they may have affected the determination of neighboring wavelengths.2803A. This line exhibits the largest difference AOW-MK. We observed

this line by means of three pairs of interferometer plates, two of which givehigh resolution while the third is thinly coated to permit the observation ofweak lines with moderate exposure. The results from the high resolutionplates agree with MK; the more numerous and highly consistent resultsfrom the thin plates differ from MK by 0.0010A.

2699.3A. In our spectrum of natural mercury (see reference 3), this linewas wrongly interpreted as being 2699.50 observed by DIjardin. The correct

exceptions that the sources were electrodeless tubes anda separator of 85 mm length was used for some plates.Our tubes were air-cooled. For the soHg98 spectrumthe line 5460.7532A was used as standard to determinewavelengths 6709-3125A. Then our observed value3125.6698A was used as standard for the region 3125-2446A. Of the wavelengths so obtained (Table I) thelines 2576A to 2464A were used to evaluate the shortestwavelengths in our list.

-Since the carrier gas was usually argon at two orthree millimeters pressure, several argon lines weremeasured against 5460.7532A. The means of thesewavelengths and those of Humphreys,2 and 6965.4307A3

as emitted by the carrier gas were used as standards forthe spectrum of 8oHg202 in the region 6907-3125A. A

tube containing cadmium and Hg202 with neon as carriergas was used as a source for a few plates. These plates

were not uased in determining the wavelengths of Hg20 2

because the temperature of the tube was increased overthe customary 30'C in order to develop a strong cad-mium spectrum.

As is well known, in making long exposures with a

neon-mercury Geissler tube as source it is necessary tocontrol the temperature if the relative intensities of thetwo spectra are to remain constant. It is even moreimportant to control the observing conditions for ex-posures longer than ten minutes when the electrodelesstube excited by radiofrequency is the source, and thespectra of two or more elements are being emitted by

the same tube. This is especially true when, as in ourcase, the image of the tube is on the slit.

The argon lines shorter than 5000A lacked sharpnesson plates taken by means of separations of 40 mm ormore. For the larger separations some of the exposureswere made alternately on 198 and 202, changing everyten minutes or less, and the thickness was determinedfrom the measurement of the 198 standard.

In Table I the first and second columns contain,respectively, for 198, the measured wavelengths in

2 C. J. Humphreys, J. Research Natl. Bur. Standards 20, 24(1938).

3 W. F. Mleggers and F. 0. Westfall, J. Research Natl. Bur.Standards, 44, 447-455 (1950), RP 2091.

wavelength in natural mercury is 2699.376 and the corresponding level,9d

3D2, is 81077.8.2653A. This line varies widely in intensity with respect to its neighbors

2655A and 2652A. We have found no reason for this variation.3983A. Mrozowski (Phys. Rev. 57. 207-211 (1940); 61, 605-613 (1942))

reports the wave number difference 198-202 as +0.957; our difference is+0.975.

2916. Mrozowski's wave number difference 198-202 is +0.447; oursis +0.443.

standard air and the corresponding wave numbers invacuum.4 The third column shows the fractional partof the differences of the levels in column six. A letterin column three indicates that this is the only line usedto evaluate one of the levels involved, 8p 3P2', in thefirst row. The fourth column contains the fractionalwavelength as measured by Meggers and Kessler.' Sixof these lines were measured by Blank; 6 no differencebetween Blank and MK exceeds 0.0002A. Column fiveshows the number of observations; here "C" indicatesthe wavelength was not observed but computed.Columns seven, eight, nine, and ten contain the datafor 202 similar to those for 198 in columns one, two,three, and five.

In setting up the levels of both isotopes the modernconvention was followed and 6s2 'So was set at zero.The data of Table II show that the low singlet "P"term, most of the "D" levels, and the higher "S" termshave nearly the same isotope shift. Lines arising fromcombinations of the singlet "P" and many of the evenlevels will have nearly the same wavelength in thespectra of all the even isotopes. Therefore the spectrumof natural mercury has several lines that are useful asstandards for all but the most exacting work. As far aspossible the levels were derived from lines in the region5790-3654A in order to minimize the effects of uncer-tainty in the value of the index of air.5 The use of theselevels to compute wave numbers for lines of wave-length less than 3000A shows large discrepancies be-tween observed and computed. Where the 0- C issmall in the short wave region, the levels have beenderived from neighboring lines. The levels of 198 and202 were derived in exactly the same manner; the differ-ences between the levels of the two isotopes are freefrom any effects of error in refraction and nearly freefrom error in phase change.

The use of the interval 6p 1Pi-6p 3 P1 which is14656.462 for 198 or 14656.495 for 202, shows that the

I W. F. Meggers and C. G. Peters, Sci. Papers Bur. Standards14, 697 (1918), SP 327.

5 W. F. Meggers and K. G. Kessler, J. Opt. Soc. Am. 40, 737(1950).

6 John M. Blank, J. Opt. Soc. Am. 40, 737 (1950).

58 Vol. 42

MERCURY ISOTOPES 198 AND 202 SPECTRA

TABLE II. Even levels of 8omercury'98 I and 8omercuryB I. TABLE III. Wave number differences Hg20 -Hg1 98.

Wave Number8oHg19s

00000.00063928.37074404.72778404.49280365.788^

62350.57373961.41778216.36380268.13381416.386

71333.33477064.23479660.91181057.881

71336.29971396.36871431.466a77084.75277108.06777129.696a79678.82179690.45579702.741a

81071.12681077.79-81085.261a81913.69-

Odd levels37645.24739412.46744043.15554068.92976823.687a78813.13279963.97781022.917'

soHg2l'

0.0008.0944.4294.1935.476

0.2991.1216.0647.8396.088

3.0303.9290.6097.571

5.9916.0611.1544.4487.7639.3858.5260.1592.444

0.8417.51-4.955a3.44-

4.9172.1342.8238.6293.3993.0893.7612.592a

Diff.

0.0000.2760.2980.2990.312

0.2740.2960.2990.2940.298

0.3040.3050.3020.310

0.3080.3070.3120.3040.3040.3110.2950.2960.297

0.2850.28-0.306

0.3300.3330.3320.3000.2880.0430.2160.325

£ Only one line was available for the determination of this level.

scales of the spectra of the two isotopes are the sameto within a few thousandths of a wave number through-out the region 5790-2378A. To illustrate, the intervalfrom 5790A (6p P`-6d D 2 ) to 3131.8A (6p P,0-6d D2)is 14656.461 in the spectrum of Hg198 and 14656.497in that of Hg202. This same interval from 3901A(6p 1P`-8d 'D2) to 2481A (6p P,0 -8d D2) is 14656.410and 14656.442 for Hg198 and Hg202, respectively. Thedifference in this interval between short and long wavesarises from error in observation, uncertainty of phasechange, and lack of consistency in the refractionformula. But the relative value of the interval is nearlythe same for long and short waves of both isotopes,showing that the scale is the same in both cases, animportant consideration in the evaluation of isotopeshifts.

After our paper was in manuscript an article by H.Barrell, "The Dispersion of Air Between 2500A and6500A" appeared in The Journal of the Optical Society of.America.8 If Barrell's formula is used, the intervals5790-3131.8A and 3901-2481A become 14656.439 and14656.431 for Hg'9 8; and 14656.475 and 14656.463 forHg202. The NBS and Barrell's formulas cross at 2450Aand there appears to be no advantage in using the new

H. Barrell, J. Opt. SoC. Am. 41, 295-299 (1951). .

X Schuler AOW-SA AOW et al. Wave No. PPM

6716 +0.229 +0.233 -0.004 0.306234 +0.062 +0.070 -0.008 0.506072 +0.237 +0.241 -0.004 0.255675 +0.057 +0.060 -0.003 0.204358 +0.060 +0.055 +0.005 0.252536 -0.333 -0.339 +0.006 0.15

formula for the region shorter than 2400A. Since re-fractive index in the region 10,000-1900A will soon beobserved at The National Bureau of Standards andelsewhere, it does not seem worth while to recomputeour tables at present. It is possible that there exists aconstant difference between the two systems amountingto three or four thousandths of a wave number. Thatthis difference is not large s indicated by a comparisonwith the wave number differences of six lines of 198 and202 found in the publications of Schuler' and associates"0who observed the spectrum of natural mercury. Thefirst four of these lines are weak on our plates and maynot conform to our scale.

In Table III the first column contains the wavelength;the second column shows the difference in wave numberof the lines in the spectra of 202 and 198, columns twoand eight of Table I; the third column contains thesedifferences as found by Schuler and associates; in thefourth column are the differences between the dataof columns two and three; and finally, the data ofcolumn four are shown reduced to parts per million, incolumn five.

The spectrum of natural mercury was observed in theregion 5790-3125A in the same manner as were thespectra of the isotopes with the exception that the elec-trodeless tube was charged with neon at 3-mm pressure;the wavelengths so determined and those previouslymeasured' with a Nutting tube as source differ in themean by only 0.0003A; no individual difference exceeds0.0015A. It appears that the sources may be used inter-changably without increasing the error inherent in theuse of natural mercury.

A few observations of the spectrum of natural mer-cury in the region of wavelengths shorter than 3125Awere made with the electrodeless tube as source. These,and our earlier list,' by comparison with Table I, indi-cate that the spectrum of Hg202 represents the spectrumof the natural element well enough for purposes ofidentification, except for the one line 2536.5A.

Our former colleague, Mrs. Jean Longwell, helped uswith the computation; Mr. Don Sieber did somemeasuring and computing; Mrs. Helen Louise Emlerwas particularly helpful.

We are indebted to the National Bureau of Standardsfor the loan of interferometer plates and separatorsand to E. U. Condon, W. F. Meggers, and CharlotteMoore Sitterly for encouragement and assistance. Wethank R. F. Mehl and the Carnegie Institute of Tech-nology for the loan of the quartz spectrograph whichwas used for this work.

9 H. Schuler and J. E. Keyston, Z. Phys. 72, 423 (1931).10 H. Schuler and E. G. Jones, Z. Phys. 79, 631 (1932).

Level

6s2

1So7s 'So8s 'So9s 'So

lOs 'So

7s 3S,8s S,9s 3S,

lOs 3S,lls 3S,

6d D27d D28d 1D29d D2

6d 3D,6d 3D26d 3D,7d 3D,7d 3D27d 3D,8d D,8d 3D28d 3D3

9d 3D,9d 3D29d 3D3

lOd 3D3

6p 3Po°6p 3Po6p 3P26p 'Pi0

8p 3P20

8p Pi'9p Pl0

lop 3P20

JanUarY 1952 59