TheX 3400 Bandof Phosphorus Hydride. By R. W. B. P...

328

The X 3400 Band o f Phosphorus Hydride.

By R. W. B. P e a r s e , A.R.C.S., Ph.D., Demonstrator of Physics, Imperial College of Science and Technology, South Kensington.

(Communicated by A. Fowler, F.R.S.—Received July 21, 1930.)

[Plate 19.]

Introductory.In the account of the band spectra associated with phosphorus* given in

Kayser’s “ Handbuch der Spectroscopie,” mention is made of a band lying between X 3476 and X 3379 which was obtained by Geuterf* from a discharge tube containing phosphorus and hydrogen.

Reference to the original paper showed that Geuter besides recording the results of an extensive investigation of the spectra produced under various conditions with phosphorus in the flame, in the arc, and in the discharge tube, had also made measurements on this band. The wave-lengths obtained, however, were only considered to be accurate to 0 • 03 A. and were quite inadequate for a detailed analysis of the fine structure of the band. I t was desirable, therefore, to re-photograph the band under higher dispersion, especially as the experimental data for triplet molecular states are somewhat scanty.

Experimental.An investigation of the conditions most favourable for the production of the

band was first made with the aid of a quartz spectrograph (Hilger’s E.2) giving a dispersion varying from 65 A. per millimetre at X 5500 to 7*5 A. per millimetre a t X 2300. Various patterns of discharge tube were tried, that finally adopted % is illustrated in fig.l. I t is essentially of the H type modified by the introduction of a small bulb with a ground-in stopper between one end of the capillary and the corresponding electrode. The tube was excited by the uncondensed discharge from the secondary of a 4-inch induction coil working on an alternating current supply (50 cycles). The heating of the tube could be controlled to some extent by varying the current through the primary. The current was usually about 3 amperes.

* “ H andbuch der Spectroscopie,” vol. 6, p. 254.•f ‘ Z. W iss. P h ot.,’ vol. 5, p. 50 (1907).J T his ty p e was suggested to th e author b y Dr. K . R . R ao’s work on “ Selenium .

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X 3400 Band o f Phosphorus Hydride. 329

This arrangement proved very satisfactory for obtaining the spectrum in the presence of hydrogen. Hydrogen from a commercial cylinder was dried

Fia. 1.— T ype of discharge tube used in th e production of th e spectrum of phosphorushydride.

by passage over P 205 (without this precaution X 2811 and X 3064 OH bands appeared) and allowed to pass in a very slow stream through the discharge tube. In passing around the electrode the gas became warmed sufficiently to vaporise a small quantity of phosphorus in the bulb and to carry it into the capillary. With proper adjustment of the primary current and the hydrogen stream no extra heating of the tube was necessary and the transport of phosphorus through the tube was slow and regular. The part of the tube carrying the quartz window at the further end of the capillary was made 2 inches longer than usual and cooled with moist blotting paper. With these precautions to prevent clouding of the window, it was found possible to give an unbroken exposure of several hours. The intensity obtained was such that an exposure of 4 hours was required for a good plate in the second order of the 10-foot grating.

A few experiments were carried out to observe the effect of replacing the hydrogen by various other gases. When the tube was freed as far as possible from all gases other than phosphorus vapour, the very extensive system, stretching from about X 3500 to beyond X 2100, which Geuter called band spectrum C M was present strongly, and is attributed to the molecule P 2- With the addition of nitrogen no further bands were observed other than those



330 R. W . B. Pearse.

attributed to N2 ; but with air, besides the N 2 and NO bands, traces of a system with principal heads a t XX 2555, 2478, 2396 and 2320 were obtained. This system was obtained much more strongly with P 20 5 in copper and magnesium arcs in air, and was identified with the system obtained by Geuter,* de Gramontf and de WattevilleJ in the arc.

I t is clearly a doublet system, which is consistent with its assignment to the molecule PO. Only when hydrogen was present in the tube was the band at X 3400, which Geuter called “ band spectrum B ” strongly developed. Under the conditions described earlier in this section this became by far the strongest feature of the spectrum.

Measurements.The wave-lengths were obtained from measurements on the best of the plates

taken in the second order of the grating. Wherever possible the iron standards recommended by the International Astronomical Union§ in 1928 were used for interpolation, but in regions where these were few, the mean values given by Kayser and Konen|| were used. In this region these values, only need reducing by 0*001 A. to bring them into line with the 1928 values. The dispersion of the grating is 2 • 7 A. per millimetre in the second order and lines were resolved down to 0*03 A. Except in the case of difficult lines the errors in the wavelengths should not be much greater than 0 • 005 A.

The Structure of the Band.The isolated nature of the band and its widely spaced rotational structure

confirm its assignment to a hydride. I t resembles the NH band at X 3360 in having a strong maximum of intensity near the centre and a very symmetrical distribution of lines, with widely spaced series emerging from each extremity. In this case, however, these series appear as doublets instead of triplets. The PH band further differs from the NH band in showing a greater number of secondary maxima of intensity. The central maximum lies a t X 3420, while there are secondary maxima at XX 3427, 3409, 3395 and a sharp edge at X 3390. The appearance of the band under high dispersion can be seen from the enlargement shown in Plate 19.

Analysis of the band leads to the scheme of energy levels shown in fig. 2. * * * §

* ‘ Z. W iss. P h o t.,’ vo l. 5, p. 40 (1907).t ‘ C. R .,’ vo l. 149, p. 263 (1909).t ‘ Z. W iss. P h o t.,’ vo l. 7, p. 279 (1909).§ ‘ Trans. In t. A st. U n ion ,’ vo l. 3 (1929).|| “ H andbuch der Spectroscopie,” vol. 7, part 1.




The lower state may be looked upon as consisting of a single set of rotational levels each split into a narrowly spaced triplet, the two lower components of

J8 --------------------------- r—

3i r 0 !J 7 --------------------n — •

3E

Fig. 2.— Energy L evel D iagram for the X 3400 B and of P H , show ing the transitions givingrise to the various branches.

which are very close and separated by wider intervals from the upper component. Such structure has been found in the 0 2 bands* and is characteristic

* Cf. R . S. Mulliken, ‘ Phys. R ev .,’ vol. 32, p. 880 (1928).

VOL. CXXIX.— A. 2 A



332 R. W . B Pearse.

of a 32 electron level. In the upper state the rotational levels fall into three sets separated by intervals of about 100 cm.-1. Each rotational level consists of two close sub-levels. The whole arrangement of levels is just that to be expected for a 3n state which closely approaches Hund’s case a. This classification is in harmony with that of the NH band at X 3360, which has already been assigned to a 3II -► 3E transition.* In the case of the lighter molecule, however, the spin fine structure is of much smaller magnitude and the 3II state tends towards Hund’s case b, the triplet spacing decreasing rapidly with increasing rotation of the molecule from about 20 cm.-1 at the origin. The fine structure of the 32 levels has not been resolved in the case of NH, but the rotational levels are, of course, more widely spaced. I t is from these differences in the relative magnitudes of the spacing of the various energy levels that the differences in the appearance of the two bands arise.

Notation and Term, Values.For the purpose of setting out the various branches and the term values

obtained from them, which justify the proposed scheme of energy levels, the full notation recommended in the forthcoming Report on Notation for Spectra of Diatomic Molecules by Mulliken is somewhat cumbersome and in this particular case can be simplified considerably. In the diagram of energy levels the transitions giving rise to the various branches are drawn so that the magnitude of the energy change increases from right to left. I t will be seen tha t from each component n level the nine transitions which occur group themselves into five branches. These are conveniently called the O, P, Q, R and S branches respectively. Each rotational level of the 3E state is given in order, a value of K starting with 0 for the lowest. The lines denoted by O(K), P(K), ..., are the members of their respective branches which have the same final rotational level K. The O, Q and S branches arise from the upper or A rotational levels of th e n states, while the P and R branches arise from the lower or B rotational levels. The O and S branches are single, the P and R double and the Q triple. The separation in the P(K) doublet is equal to that between the first two members of the Q triplet while the separation in the R(K) doublet is equal to that between the first and the third. The fact that the separations are equal for equal values of K indicates that this fine structure arises in the E state. The three components of the rotational levels are distinguished by calling them F l5 F 2 and F 3 levels such that the O transitions are

* Cf.R. S. M ulliken, ‘ P hys. R ev .,’ vol. 33, p. 730 (1929).




to Fx levels, the P transitions to Fi and F 2 levels, and the Q to F 1} F 2 and F 3 levels. The R transitions are then found to be to F 2 and F 3 levels, and the S transitions to F 3 levels. The lines are distinguished by such symbols as Q1(K), Q2(K), •••> etc., according as the transitions are to F 1? F 2, ..., levels.

The nine transitions from each of the three component levels 3II0, 3II1 and 3II2 are defined thus :—

6 X (K) = F 'a (K - 2) - F ' j (K) + 4 G

(K) = F 'b (K — 1) — F "1)2 (K) + T- + G

Q1>2.3 (K) « F 'a (K) - F "1i2i3 (K) + T- + G

R 2>3(K) = F 'b (K + 1) — F " 2>3 (K) + T « + G

S3 (K) = F 'A (K + 2) - F " 3 (K) + T* + G.

The F terms represent rotational energy while Te and G represent amounts of electronic and vibrational energy which are constant for the whole band.

The rotational term differences A1F(K) and A2F(K) for any energy term F are defined as follows :—

AXF (K) = F (K + 1) - F (K)

A2F (K) = F (K 4- 1) — F (K — 1).

For the 3II state there are in all six rotational energy functions, viz., FA and Fb for each of the three component levels. The A2F values can be obtained directly from the following line combinations :—

A2F 'a (K) = Q, (K + 1) - Oj (K + 1) = S3(K — 1) - Q3(K - 1), A2F 'b (K) = R 2r(K) - P 2 (K).

The values of AXF'(K) cannot be determined directly but the following relations hold :—

AxF 'ab (K) = F 'a (K 4 1) - F 'b (K) = Q1>2 (K + l ) - P 1>2 (K 4 1)= S3 ( K - 1) - R 3( K - 1).

AxFba (K) = F 'b (K 4 1) - F 'a (K) = Px (K 4 2) - Ox (K 4 2)

= - 2, 3 (-^) Q2, 3 (F )»2 A 2




If FA = FB then Aj Fa-r (K) = AxFba (K) otherwise

i [ AiFju, (K) - A ^ ba (K)] = i [Fa (K + 1) + FA (K)]h [®b (K + 1) -j- F b (K)].

This quantity which may be called SAB (K) may then be taken as a measure of the magnitude of the AB doubling.

For the final 3E level there are three rotational energy functions F "1( 2i 3. The A2F"(K) values are obtained from the relations :—

AaF"* (K) = Qj (K — 1) — O, (K + 1)A2F " 2 (K) = E 2 (K - 1) - P 2 (K + 1)

A2F 3 (K) = S3 (K 1) — Q3 (K -f~ 1).

The three sets of O, P, Q, It and S branches yield three values of each of these quantities which should agree. The AXF (K) values have not been evaluated as they have no special significance.

The term differences obtained according to the above equations are set out in Tables I to V III.

Table V III.—Mean Values of SAB (K).

K. 3J72 -> 327. mx su. 3170 -> S2J.

01 0 1 2 O i l2 0 -16 0-38 0 1 33 — 0-58 —0 064 0-21 0-64 0 025 0-42 0-73 —0-236 0 -46 1-06 0-197 0-72 1-18 0-018 0-83 1 1 4 —0-479 1-00 1-24 —0-41

10 1-29 1 0 5 —0-19



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O8 JS & 2 8, »• 0 s oo h©

© oH-H

d o

« 0 OQ O

-S II o©

5o£ce.2>>*5 ?

©pd

TOseg&PL,eg

. I I® > © oH § ■*? ■**l o l l

^ 5*c> ©

a so ^■» 003 ifc«

- d d

QQ CO © © ■+S +-»eg eg o ©*3 *33 dHH HH



338 R . W . B. Pearse.

S' l

a ii< fCQ

O O r ^ ^ i O l > C C i O i O O H C O H ( O I > C O H 0 5C O O O r H P ^ C O C O ' ^ ^ O ^ P ^ O W i O O O Oo o s o i o o a o o o o o o o c b c b t ^ i i o ^ G N i o c o0 < M » O O O H ^ b - O C O « 0 0 ) ( M » O C O H ^ C O h h h h C ^ N ^ I C O C O C O C O ^ ^ T t < » O l O i O

S' 1

GO

0 4 ^ * O l O t ^ 0 4 0 O a } 0 C > l O G 0 © 0 4 l O 0 4 0 0 O r H H l O C O O O N O ^ W W W W H i O O J O ^ WM X ( N I > C ^ ^ C < | t ^ ( N I > ( N t ^ W C O O i o d 5 ^' ^ i O t ^ X O ' H C O ' ^ C D t ' a i C H N C O l O C O t ^ O J

h h h h h h h ^ i ^ w ^ I N N

OP

ta

S \ § i «*

^ 0 5 P 0 0 i O t ^ C D ( N i 0 e 0 ? 0 < ? 5 O O 0 0 H 0 0O O ^ C O O O J O I O W ^ O ^ M O O H C C ^ H I O( N t ' C q C D H C 0 H C 0 H » 0 O ^ 0 5 C 0 l > H H < T * I I O I > O O O H C O ^ C O ^ P O H « ^ C O I >

r-H r-H r-H r-H r-H p-H pH (M 04 04 04 04

<M

cCO

.2CQo>

M ' n% p< *10 "ST

t ' ’%C 4 T ^ © t > t ' * * O t ' - © r-H r-Hi O O C ^ ^ t ^ l O O O ( M C O r-H

© © © o b c o o o a b a b t ^ I t ^ - oO C < J I O O O h ^ 1 > O M 05 04pH »*H r-H r-H 04 04 04 CO CO CO

ofl<ua>Stt

Qa§

MM ^-3 O’£ & 1 ^ hM

Ph

H H i r f f C O H C O O i O H O l Ci OOO ^ O H O S ^ C O ^ O ^ O O t > COW I > G S | i c i c O H C D H l i | Oi' ^ » 0 ^ 0 0 0 ' H W ^ C 0 1 > © r-H

p H pH pH pH r-H p H 04 04

EhISA.2c3-4-3oP3

1 = 1

^ ^ 1 o>

l O O O H O O H O O P C O O C O ( N f f OO C O C O O H O O W C Q I O C O OC 0 t ^ C 4 l > ‘ O 4 l > O 4 l > O 4 l > * O 4 t ^^ l O ^ O O O > H C O ^ ^ ) l > O i O

pH r-H r-H r-H pH p H r-H 04

Tabl

e IV

.-

f ts rSvH 1 '-5^ 1 o>

133-1

815

9-64

188-8

121

8-94

248-

6727

8-65

W +

* -$ 7<y

72-51

87-1

210

2-03

117-

3013

2-07

147-3

8

w +Hcj, £4£ + orq« 1

Ph

72-52

87-7

810

1-64

116-6

013

1-27

w



Tabl

e V

.—R

otat

iona

l Ter

m D

iffer

ence

s fo

r 3IL

Sta

te.


S J f

1

m 1

109-

8714

2-21

174-

0920

5-67

237-

2926

8-96

299-

9533

0-65

361-

2539

0-25

1 i > a o i o i o o o c o c ^ a o i > » c & i o r—t e o ^ t i c o c o < M r H C ^ c o i o c *

( N I > M O O I O H I > W Q O M O O CO rfl <X> t> C* i—i <N iO 00

rH rH rH rH pH rH

W'w" eo

fe w I ' V

( N C D H H I > O O X C D O 00 JO ^ H h iO O CO

CO W G O ’i o c O H t ^ C O

rH rH rH rH rH

— w M "

1THj (M

P5

e o a o r t i i a o i o a o o G *< O O C 5 h ( N H i O h ®

o b o f H c i u o ^ o b i o^ H ^ h O C O C O O J C O

H H H < M < M < N < N C O

£ £ <M

v«—O’ f»tW | t T c

«

O S ^ C O O H < M H O O O < MC0COQOcDlO<NO**OrHHft

O I X M O O ^ O l O H M nC 0 ^ C 0 I > 0 5 H

rH rH rH rH rH

£ _ +w

iO'

<Oh t ^ t} J 1 0 ^ 0 I > I > ^ C O tJ<< M < M C OG Ô <M O Ô O îO Q OC O

H CO Oi lO H l> <M 00 CO 00 ^C 0 ^ C 0 J > 0 5 H < M ^ » 0 t > 0 0 O

H H H H H H

w

rVi *®*W o

1o>

J 0 O J 0 < 0 ^ < 0 C 0 0 l < M 0 1C O l O G ^ X t ^ C O ^ O i C O O O

o b o ^ M C O i C l H o b o i O O» > H tM > O C 0 < 0 0 5 C 0 C 0

h h h c ^<m <m c ^ coco

* ,M pTP I

0 ) ® H h * ^ ^ l O C 5 < M C O ^c o W J O C O H c q n t ' C O i O C O

H l > C O C 5 l O H I > ^ O O C O Q O C O '^ C O I > O 5 H ( M ' , l O l > Q 0

rH rH rH rH rH rH

_ S5* M +

•<©* &

4 fiAh

C 5 0 5 0 0 C J h * H ^ ^ C 5 l 0 O < M ^M C i O O h ^ t M C O ^ O ^ X O J O O

H C © < N 0 0 T t ( O * O H t ' » < N t ' - < N f c ' ’»c o ^ c t ^ O J H c q ^ i O t ' X O ' H

rH rH rH rH rH rH (M

* O H ^ C O ^ » O O J > » O i O H ( M C OrH rH rH rH

■.:.■■ Vi-, ‘I '■ ; ..; ■■




1 0 00 ^ o10 o ©* <x>pH I—|

M iV 1% 4 «

102

36-3

454

-14

71-5

488

-68

<pc6

S ' ^ 2 o*

\4*«

36-0

153

-91

71-4

088

-81

122-

57

zn©

eCOMOMHCGa>

S 'HH ^5: * *

s-4 I «PHP3

OWWH^WOO® Ct> CO CD p-H CO CO 1C CO ^0150*00^^0^^ »0 05W<0 05^C0 05W HHH^êqco

Paa>

.a?£fc3sa5

— fc? >•»>*y o*

* J d'-s«

36-4

253

-96

71-5

288

-71

105-

6912

2-21

138-

5615

4-58

170-

44

H*13a#o

*43c«-g

*2

W +»i-H PH'",+ Z s%iW ^

CP

OOOOiHOCOWOOUJW^WH^CO’ OiOO'-*cbco i-HGOiCcHob'4<c>|HC0 10I>«0^«10^ pH pH pH pH pH

Tabl

e V

I.-

m " +

f e t■ w i

C?

O0Hl£D«Oh*H0O W*OO5t ^^^HOSlOWOOCOO OS ©*4<o»oocl5ôc!i4<ih'i>*0C5N®05N©05C^»0XH

h h h N^ÎCOCOCOtH

& + •W*-—K>l «pH PH& ?+ S f* - S i

9

COO' WMCOCOCO«’ Wt^*Ot'O*O0O'^00HHO*O*O^COrHHOO»f5H<X)^0*00H«*0^000^w*0^000pH pH pH pH pH rH (M

w +

C + 5 1Ph

QOI>COCOHIOCO' 05*OC<1t^HCiiOiOCOôOiOiOt't *coco»-HobiOcsiQb'4<o»cp-tCOlO OOOfMOOlOt'OO pH pH pH pH pH pH

w O*—ie C0 U5?0t 0005OrH©5|

b i gi

COOQ



Tab

le V

II.—

Rot

atio

nal T

erm

Diff

eren

ces

for

32 S

tate

.


pH

M +

r W 1 60

* 4 ?t o

OQ

49-9

283

-79

117-

63

l

«©

1

fcft o

M +

> i ^

1

A3

CO O lO H H H © O i a © p H ^ t - t > F * l f t

0 5 0 5 t ^ H ^ t > » O C 0 < 0 ^ O O H I O X H I O O O H

pH pH pH (M ©q CO

s — +

r - r w

C O C O t > C O H O O I C O O O Oh * ? D ^ i O O i O O ^ C O i O

C O I > pH ^ I > pH ^ C 0 0 5 pH O O H i O Q O H l C X H ^ X

H h H (N W CO CO CO

£ ~ +

f aO '

^ |CQ

C O C O l O O O t ^ C O ^ C O O O © * ©c s i > » o x c q x o i ^ ^ H c o

O C C b * O ^ ^ O C O X C 5 p HT H X H I O X H I C X ^ ^ X

H H H

t o

1

?

tad "t"

> i

T j S ; |

Ah

© q ^ i > © q o o a o ^ o o t > o ©* a a o © © q i > * f c ^ a o © « - H » c

© O t r » p H H t < l > - © C © © © p H X H I O X H O X H ^ X

H H H d W W W « W

5 " +

r ~ «

f a J . c T

O '

i © © © t ^ © H * © C © © © i Q ©l O © C O t ^ © © Q O © M < O O Q O i O

X H t Q X H l O X H ^ X H ^ H H H W C O X W ^ ^ I

M +

P f f M .

5 * 1 o >

t oOQ

© p H © c © c © © q i © © © © q © T * © © ©© t - * C © C O © t ^ © t O © * O i O ^

© C 0 t > - © ^ l V © C © C 0 © « - H C © * 0l O X H l C X H l O X H ^ X H ^

H H H W ( N W C C C 0 « ^ ^

t o

1Cl

t ?t o

S " “1“

> i ^

^ ' -S 1

P3

t ^ © q ^ © © © © ©< ^ © S O © Q O

^ I t* pH ^ ^ - © c© © X H l C X H l O X H

p—< pH i-H © OQj © CO

5 " +

r - 7 ^f a * o

o

218-

0626

1-07

284-

1431

6-98

w© p H © q c O ^ * O © t ^ a 0 © © p H O * C O

H pH pH pH

Tab

le V

III.

—(S

ee p

. 33

4.)



342 K. W . B. Pearse.

Discussion of the Electron States.In the following discussion of the electron states involved in the emission

of the PH band the notation used is as far as possible in accordance with that recently agreed upon by band spectroscopists.* Also, in order not to burden this paper, which deals with a particular case, with too much material of a general nature, it is assumed that the reader is familiar both with this notation and with the general theory of molecular energy levels. For further details on these matters the references given above should be consulted.

The Final State.The structure of the band in respect of number of branches, their spacing

and intensity distribution, is tha t associated with a transition between 3II and 32 terms while the nature and magnitude of the fine structure and the form of the rotational term differences appearing in the final state show that it is of the 3£-type. In 3S states the energy equation to be expected is a slightly modified form of that for Hund’s case h multiplet states. In case h states the resultant spin electronic angular momentum S is coupled to the axis of the angular momentum K which is the resultant of A, the component of orbital angular momentum along the electric axis, and O, the total angular momentum perpendicular to the axis. This gives the quantum number J representing the resultant angular momentum of the molecule, and whose possible values are

J = K + S, K + S - l , ,.. IK — SI ,

where the values of K are given by

K = 1 A ! , lA j + 1, | A | + 2, ...

For a 3S state as here considered A = 0 and S = 1 so that K has all integral values starting from 0, and for each value of K there are three values of J = K,K ± l .

* The substance of th is agreem ent is shortly to be published in an article in the ‘ Physical R eview ’ by R . S. M ulliken, “ R eport on N ota tion for Spectra of D iatom ic Molecules. A n account w hich needs on ly slight revision is also given b y R. S. Mulliken in * R eview of Modern P hysics,’ vol. 2, N o. 1, p. 60 (1930). A preliminary account appeared in the “ D iscussion on Molecular Spectra,” * Faraday Society Trans.,’ pp. 628-633, 770-772, and E rrata (September, 1929); also in book form (Gurney and Jackson, 1930).



The general term value given by Mulliken* for case b after omission of a term in A is

T = T* -h G 4- [K (K -j- 1) + G2] + / ( K , J — K) + (K, J)

+ D„K*(K + 1)2.

In this equation Te is constant for a given electronic state and represents the electronic energy ; G is constant for a given state of vibration in the electron state and represents vibrational energy. This must not be confused with within the bracket which represents the contribution to the rotational energy of a rapidly varying component of electronic angular momentum perpendicular to the electric axis. I t is of no practical importance, as it cannot be separated in the analysis from Te and G. The part

F = B„ [K (K + 1)] + (K + 1)2

represents the rotational energy of the molecule as a function of K. B„ and D„ are constants for a given value of the vibrational quantum number v. The small term <f> (K, J) arises from interaction between the electronic angular momentum G and the nuclear rotation. Its usual effect is to cause a slight change in the value of Bv or to make K depart slightly from integral values. The remaining term / ( K, J — K) represents the interaction of the spin S with the rest of the molecule which gives rise to the three components F x, F 2 and F 3 for each value of K in the rotational term. The subscripts are added so that for F 1} F 2, F 3, the resultant J = K + S, K, K — S, where S = 1, that is so that J — K = 1, 0, — 1. The interaction of S with the small magnetic field developed parallel to K gives rise to a term f

y/2 {J (J + 1) - K (K + 1) - S (S + 1)}.

In addition to this KramersJ has shown that there is an energy of interaction w(K, J — K) of the individual spins which make up the resultant S when this

is greater than For 3E states he obtains :—

w (K, + 1) = — s [1 — 3/(2K + 3)]; w (K, 0) = + 2s ;

w (K, — 1) = — e [1 + 3/(2K + 1)].

* ‘ R eview s of M odem P h ysics ,’ vo l. 2, p. 106 (1930). The notation used in the present paper differs sligh tly from M ulliken’s in accordance w ith the more recent recom m endations of the R eport.

t Cf. E . C. K em ble, “ M olecular Spectra in G ases,” pp. 346-347, * B u lletin N at. Res. Council U .S .,’ N o. 57 ; also J. H . van V leck, ‘ P hys. R ev .,’ vol. 33, pp. 498-500 (1929).

t ‘ Z. P h ysik ,’ vo l. 53, p. 422 (1929).




344 R. W . B . Pearse.

Combining this with the above term

/ (K, + 1) = yK — e [1 - 3/(2K + 3)] ; (K, 0) = - Y + 2e ;/ ( K, - 1 ) = - y (K + 1) - e [1 + 3/(2K + 1)].

I t will be noticed from these expressions that the behaviour of the term in e is quite different from that in y with increasing value of K. In the former, the states with J = K ± 1 form a narrow doublet whose separation decreases with increasing K and whose centre is separated from the state J = K by the approximately constant interval 3s. In the latter the states with J = K f 1 diverge from the state with J = K by the increasing amounts y (K + 1), — yK. Turning to the experimental data for PH it is observed that the state J = K is well separated from the J = K ± 1 states, and also that these latter states show increasing separation with K. The actual separations can be well represented by the above formulae using the values

5 = 2-14, y = — 0-072.

In fig. 3 the curves are plotted from these values while the points represent the observed separations.

c m 10-00-

K - > 5 10 15I

- - - -

1-00-

x^

2-00-

3-00-

k\ ^

9 ' /

#iI

I§|

__©

4-00- I

f

F ig. 3.— Comparison of the observed and calculated values of the fine structure triplet separations in the 3£ level of the X 3400 band of P H . The curves represent the separations calculated from the formulae / (K , + 1) == yK. — e [1 — 3 /(2K + 3)] ; / ( K , 0) = — y + 2s ; / (K , — 1) = - y ( K + 1) - s [ l + 3 / ( 2 K + 1 ) ] , / ( K ,0 ) being taken as axis of reference. The points represent the observed values. In the above ormulae th e values obtained for the constants were e = 2 • 14 cm."1, Y =* ® #0^2 cm. .



X 3400 Band o f Phosphorus H ydride. 345

The rotational term differences for the 3S state are well represented by the following values of the rotational constants

B0" = 8-411 cm ."1 D 0" = 4-28 X 10-4 c m .'1wlicnco

I 0" = 3-293 X 10-40 gm./cm.2 r"0 = 2-06 X 10-8 cm.

since the X 3400 band is the only one observed no direct value of <o0" has been obtained. The well-known relation

D 0 = 4B03/<o02

however leads to the value co0" = 2380 cm.-1.

The In itia l State.

The initial electron state shows three sets of rotational levels separated by intervals of about 100 cm.-1. For a compound of the molecular weight of PH such large spacing is only to be expected for a 3n state. The form of the rotational term differences suggests th a t this level is an example of H und’s case o. In case a the spin S is quantised with reference to the electric axis, on account of the magnetic field along this axis produced by A. This gives rise to a quantum num berS which takes the values— S, — S -f- 1, ... S. This quantum number is then combined with A to give a resultant £1 = \ A + S | , which combined with 0 forms the resultant angular momentum of the molecule represented by the quantum number J . This takes the values

J = Q ,Q + 1, + 2, ...

For a trip let level S = 1 so th a t there are three values of Q, viz., 0, 1 and 2. The energy term for this case is

T = T 6 + G + A AS + B„ [J (J + 1) — a 2 + G2 + S2perp.]+ 4>t (S, J) + D„J2 (J + l)2.

Here different values of S in the term AAS give the different components of the molecular electronic multiplet. The term <f>i (S, J) has two values <j>A and

<f>B for each value of S and J and gives rise to the so-called A-type doubling of each of the rotational levels. These two components are the A and B levels of the previous sections. The magnitude of the doublet separations are indicated by Table V III.

Approximate values of B1?/ for this state have been calculated as follows. I t is assumed th a t D„/ will be about 4-0 X 10 4 cm. 1. The amount




D[(K + 1)* 2(K + 2)2 - K2(K - l)2] is then added to the values of A2F'(K) from Tables IV to VI, and the sums divided by 4 (K -J- i). This procedure leads to the values given in Table IX.

Table IX .—Rotational Constant B for 3I1 Level.

K. 3n 0. *nv zn 2.

1 9 0 82 9 0 3 7-873 8-96 7-90 7-194 8-92 7-92 7-275 8-76 7-92 7-266 8-79 7-95 7-307 8-73 7-96 7-348 8-67 7-96 7-379 8-62 7-97 7-40

10 8-57 7-95 7-43

The results show that B depends very considerably upon the value of 2. Further, while the values obtained for the 3II1 levels are very nearly constant,as they should be, the values for the 3II0 levels decrease, and the values for the3n 2 levels increase, with K. This probably indicates that the 3II state is not completely case a but tends toward case b.

The values of II (0, 1, 2) have been assigned to the levels under the assumption that the 3II level here occurring is inverted. This is justified by examination of the first lines of each branch. For £1 = 2 the only line with K = 0 should be S3(0) ; for 0 = 1 there should be S3(0), R 2(0) and R3(0), while for 0 = 0 the lines Q2(0) and Q3(0) should also appear. For K = 1 additional lines should appear thus : for 0 = 2, R 2(l) and R3( l ) ; for 0 = 1; Qi(l), Q2(l) and Q3( l ) ; and for O — 0, P ^ l) and P2(l). Not all of these lines have been observed owing to overlapping with other lines or to their low intensity, but sufficient of them have been found to establish the assignment of O as may be seen from Tables I to I I I .

The magnitude of the constant A in the term A A2 can be obtained from the early members of the branches by using the expression for the energy term given above, neglecting the small factors this is

T = const. + A AX + B [J (J + 1) — a 2] + ...



347X 3400 Band o f Phosphorus .

The lowest values of this are, omitting the constant:—

J. sn Q. 3/7r 5/7a.

0 - A1 - A + 2B 0 + B2 — A + 6B 0 + 5B A -j- 2B3 — A + 12B 0 + 11B A -f 8B

From this table it is seen tha t

3n 2 (2) - m , (i) = 3n x (i) - 3n 0 (o) = a + b ,

so that by subtracting the appropriate value of B from differences between the wave-numbers of lines originating in transitions from the above levels to a common final level the value of A may be determined. A similar process may be carried out for higher members. In this way it is found that for

2n 2 -> 2U 1... A = - 121 cm .-1

2II1->in 0 ... A = - l l l c m . - 1.

The discrepancy would appear to indicate the necessity for a further term in 2, probably as a result of a tendency toward case b.

Notation.In the simplified notation used here stress has been laid on the value of K

and 0, P, Q, R, S have been used to indicate AK == 2, 1, 0, —1, —2. In the full notation these letters are used to indicate these values of AJ, the value of AK being indicated by a similar letter placed as a superscript . Also instead of K being placed in brackets after the main symbol the value of J is usually indicated. For a comparison of the two notations the symbols for the transitions shown in the energy level diagram are given in a table below.

Table X.—Comparison of Notations.

Simplifiednotation.

Full Notation.

377x -> *£. 3n 0->

0,(6) °Piai(5) °P2ai(5) °P3A1 (6)Pi (6) pQibi(5) PQ2bi (5) PQ3B1 (®)P* (6) PPlB2 (6) PP2B2 (6) PP3B2 (6)Qi(6) QRiAi (5) qR2ai(5) QR3Al(5)Q*(6) qQia2(6) qQ2a2 (6) qQ3A2(6)Q,(6) qPia3C) qP2A3C) «PSa3(7)R*(6) RRiB2<6) kR2b2 (6) RsBS! (6)P*(6) RQlB3 (0 eQ2B3(7) RQ3B3(7)S,(6) sRiasC) SR2A3(7) sR2a*(7)

■--------vol. cxxix.—a. 2 B



348 R . W . B. P earse .

Catalogue of Lines of PH .Table X I contains a general catalogue of tbe wave-lengths measured in

the A 3400 band of PH. The corresponding intensities, wave-numbers and classification in terms of the simplified notation are given in the second, third and fourth columns.

Table X I.—Catalogue of Wave-lengths.

A (I.A.). i. V. Classification.

3i7 a — aK »ni - 327. 3i7 0 - 327.

3371 152 1 29654-96 S3( l l )71-924 1 648-17 R a(9)73-350 1 635-64 S8(10)74*216 2 628-03 R 2(8)75-835 i 613-83 S8(9)75-999 —i 612-38 S8(3)76-264 —i 610-06 B s(7)76-569 2 607-39 R*(7)78-454 2 590-87 . Sa(8)78-698 0 588-73 R s(6)79-001 4 586-08 R 3(6)80-378 0 574-03 S 3(2)81-192 5 566-91 R 3(5) S s(7)81-452 5 564-64 R a(5)83-674 2 545-21 R 3(4)83-946 5 542-85 R*(4)84-059 5 541-86 S8(6)84-734 0 535-97 s 3( i )86-140 3 523-70 » 3(3)86-398 5 521-45 R a(3)87-041 7 515-78 S3<5)88-576 5 502-49 R 3(2)88-822 5 500-34 R 3(2)89-024 —1 498-50 S 3(0)90-069 3 489-49 Qi(13)90-143 8 488-84 Qi(12) Sa(4)90-220 3 488-18 Qa(12)90-382 2 486-7790-467 4 486-03 Q i( i l)90-636 2 484-56 Q3(11)90-809 6 483-05 Qi(10)90-950 3 \ 481-83 R 3(1)90-971 3 / 481-65 Q3(io ) ,91-186 3 479-7891-235 7 479-36 R-a(l)91-421 4 477-73 Q3(8)91-722 8 475-12 Qi(8)91-914 6 473-45 Qa(8)92-244 7 470-59 Qi(7)92-445 6 468-83 Qa(7)92-753 0 466-16 - Q3{6)92-790 8 465-84 Qi(6)93-017 8 463-87 Qa(6)93-214 3 462-16 R 3( 0 ) ; Q„(5)93-349 U \ 460-99 Qi(5) Sa(3)93-439 0 / 460-20



X 3400 Band o f Phosphorus Hydride.

Table X I—(continued).

349

A (I.A.). i . V. Classification.

3/72 - 327. 3/7, - 327. 3770 -

3393-536 i 29459-36 R2(0)93-583 10 458-95 Q2(5)93-776 2 457-2893-877 7 456-40 Qi(4); Qa(4)94-137 11 454-14 Qa(4)94-350 8 452-30 Qi(3); Qa(3)94-624 11 449-93 Q2(3)94*685 1 449-3994-778 1 448-58 Qi(2); Q,3(2)94-881 0 447-69 R3(10)94-979 2 446-8495-032 10 446-38 Q2(2)95-096 2 445-82 Qi(i); Q3(i)95-314 11 443-94 Q2(i) R2(io)95-740 3 440-24 R 3(9)96-070 4 437-38 R2(9)96-632 8 432-50 R3(8) S3(17); S3(16)96-656 8 432-30 S3(2)96-795 2 431•10 S3(18); S3(15)96-929 7 429-93 R2(8)97-119 2 428-29 Pi(D S,(14)97-446 5 425-46 P 2(l)97-599 11 424-13 R3(7) S3(13)97-908 8 421-45 R2(7)98-296 3 418-10 S3(12)98-684 10 414-74 R3(6)98-921 4 412-69 Pi(2)98-986 8 412-13 R2(6)99-149 6 410-72 S3(H )99-229 6 410-02 P2(2)99-865 11 404-52 R3(5)

3400-098 6 402-51 s 3(i)00-148 11 402-08 Ra(5) S3(10)00-590 8 398-26 Pi(3)00-872 8 395-82 P2(3)00-989 2 394-91 0,(2)01 •145 11 393-46 R3(4)01-337 10 391-80 S3(9)01-420 7 391-08 R2(4)02-139 10 384-88 Pi(4)02-386 8 382-74 P2(4)02-513 11 381-64 R3(3)02-680 11 380-20 S3(8)02-773 3 379-40 R2(3)03-588 11 372-36 Pa(5) S3(0)03-664 3 371-7103-825 5 370-32 P2(5)03-995 10 368-85 R3(2)04-212 11 366-98 R2(2) S3(7)04-780 3 362-09 0,(3)04-977 12 360-38 Pi(6)05-201 4 358-45 P 2(6)05-587 11 355-13 R 3(i)05-852 2 \ 352-84 R*(i)05-915 1 2 / 352-30 S3(6)06-304 2 \ 348-9406-328 1 I V 348-73 Pi(7)

2 b 2





A (LA.).

3406-54207-32007-69207-8100 7 - 8790 8 - 3940 8 - 9530 9 - 065 09-238 09-385 09-451 09-712 09-8080 9 - 91610- 070 10-277 10-479 10-541 10-654 10-81710 - 8691 1 - 113 11-462 11-547 11-770 11-89811- 93312- 233 12-29512- 51313- 052 13-141 13-351 13-478 13-63013- 95414- 093 14-292 14-768 14-79414 - 97915 - 104 15-116 15-274 15-31415- 57116 - 108 16-291 16-45416- 80717- 354 17-567 17-614 17-68217- 92818- 636 18-980

*. V* Classification.

s/r8 - an t - 3n 0 - ®s.4 29346-895 340-198 336-99

11 335-973 335-374 330-957 326-148 325-183 d 323-686 322-433 321-850 319-61

11 318-7811 317-862 316-53

lOd 314-757 313-017 312-482 311-527 310-117 309-678 307-575 304-575 303-847 301-925 300-835 300-53

12 d 297-954 297-42

11 295-5411 290-92

3 290-1611 288-35

4 287-270 285-962 283-182 281-998 280-28o \ 276-20

1 1 / 275-981 274-39

273-324 / 273-224 \ 271-87

1 3 / 271-520 269-321 264-711 263-157 261-753 258-720 254-040 252-22

12 251-8212 251-24

2 249-1410 243-082 240-13

P*(7>

Pi(8)P a(8)Oi(4)

Pi(9)P a(9)

Px(10)

P*(10)

Oi(5)P i(H )

Pi(12)

Oi(6)

Oi(7)

R a( 0 )

S*<5)

Qi(l)Qs(2)

Qx(2); Qa(l) Qa(2)

Q i(3); Qs(3)

Qa(3)Qx(4); Qa(4)

Q a(4)

Qa(5)Qx(5)Qa(5)Qa(6)Qx(6)Qa(6)

Qa(7)Qx(7)Qa(7)Qa(8)

Qx(8); Px(2) Qa(8); p,(2)

Ss(4)

S,(3)

Qa(9)Qx(9)Qa(9)Ox(2)

Qs(10)

Qx(10)

Qa(10); Px(3) Pa(3) Qa(H) Qi(H) Qa(H)

Qa(12)Qx(12)

Qa(12); Px(4) Pa(4)

Qa(13); Ox(3)

S,(2)

S8(l)





351

A (LA.). Classification.

3/7 2 - 327. 3J7j - 327. 3i7 0 - *27.

1419-063 4 29239-4319-571 11 235-08 R 3(6)19-590 11 234-92 R 3(7)19-708 11 233-90 R 3(5)19-825 11 232-91 R s(8)19-893 3 232-33 R a(6 ); R a(7)19-995 3 231-46 R a(5)20-070 9 230-81 R 3(4)20-131 2 230-30 P i(5) R a(8)20-216 9 229-57 R a(9)20-360 9 228-33 P a(5) R a(4)20-553 3 226-69 R a(9)20-683 11 d 225-60 S3(0 ); R s(3)20-782 6 224-73 R 3(10)20-943 9 223-36 R a<3)21-128 2 221-77 R a(10)21-486 1 \ 218-7221-518 1 2 / 218-44 R 3(2)21-778 11 216-23 R a(2)21-883 0 215-32 R a( l l )21-950 6 214-76 0 ,(8 )22-154 2 213-0222-401 6 210-90 R 3(12)22-659 12 d 208-70 p ,(6) R 3( i)22-876 12 d 206-86 P a(6) R a(l)23-181 2 204-25 0 ,(4 )23-444 5 202-01 R 3(13)23-820 0 198-80 R a(13)23-916 1 197-9824-440 0 193-5124-648 5 191-74 R 3(14)24-823 1 190-2424-995 0 188-79 R a(14)25-258 9 186-54 0 ,(9 )25-304 9 186-15 P,(7)25-521 7 184-30 P a(7)25-816 0 181-7926-005 2 180-18 R 3(15)26-499 5 175-9726-543 2 175-60 Qa(2)26-822 10 173-22 Qa(2)27-165 0 170-3027-422 8 168-11 Q ,(3); Q3(3)27-504 4 167-42 0 ,(5 ) R 3(16)27-690 11 165-84 Qa(3)27-853 0 164-4528-022 7 163-01 P,(8)28-217 6 161-35 P a(8)28-561 12 d 158-42 0,(10) Qs(4 ) ; Q,(4)28-824 12 d 156-19 Qa(4)29-223 1 152-80 R 3(17)29-902 1 2 \ 147-02 Qs(5)29-936 0 / 146-74 Q,(5)30-196 12 144-53 Qa(5)30-823 6 139-20 P,(9)31-010 6 137-61 P a(9)31-095 0 136-89 R s(18



352 R . W . B. P earse .


A (LA.). i.1

V. Classification.

3it2 - 3s . an t - ®i70 _ »z.

3431-491 12 29133-53 Q3(6)31-569 0 132-87 Qi(8)31-798 12 130-92 Qa(6)31-909 8 129-98 Ox( l l ) Ox(6)32-477 2 125-16 Px(3)32-756 2 122-79 P a(3)33-281 i i 118-35 Q3(7)33-382 0 117-49 Qi(7)33-597 11 115-67 Qa(7)33-688 3 114-90 P x(10)33-880 5 113-25 P 2(10)35-263 12 101-55 Ox(12) Q,(8)35-358 2 100-74 Q i(8); Pi(4)35-586 11 098-81 Q s(8); P a(4)36-428 4 091-68 Ox(7)36-670 3 089-62 P i(H )36-838 4 088-21 P a(H )37-389 0 083-5537-412 8 083-35 Q3(9),37-569 0 082-02 Qi(9)37-757 8 080-43 Qa(9)38-491 2 074-23 Pi(5)38-728 8 072-22 Ox(13) P 2(5)39-715 0 063-88 P x(12)39-738 9 063-68 Q3(10)39-889 3 062-41 P a(12) Qx(10)40-084 5 060 -76 Qa(i0 )41-026 4 052-80 Ox(8)41-862 2 045-75 Pi(6)42-089 4 043-84 Ox(14) P a(6)42-222 8 042-71 Q3(11)42-575 3 039-73 Qa(H )42-887 1 037-10 P x(13)43-043 4 035-79 P 3<13) ^44-852 6 020 -54 Q3(12)45-195 3 017-65 Qa(12)45-455 2 015-46 Pi(7)45-681 9 d 013-56 Ox(15) Ox(9) P a( 7 ) ; Ox(5)46-114 2 009-9146-147 1 009 -64 P x(14)46-285 3 008-46 P3<14)47-626 6 28997-19 Q3(13)48-003 1 994-01 Qa(13)49-261 1 983-44 Pi(8)49-465 4 981-73 P a(8)49-531 1 981-17 P x(15)49-657 2 980-11 P *<15>50-477 3 973-23 ° i ( 10) g t(J )50-548 3 972-64 Q3(14)50-933 1 969-41 Qa(14)53-028 0 951-83 P x(16)53-151 1 950-79 P *<16>53-251 0 949-95 Pi(9)53-349 0 949-1353-443 5 948-34 P a(9)53-624 3 946-83 Q3(15)54-019 1 943-52 Qa(15)





353

A (I.A.). i. V. Classification.

3I72 - 827. 8/7 x — 327. 3i7 0 - 327.

3455-330 3 28932-53 Ox( l l )55-791 0 928-68 0 ,(7 )56-750 0 920-6556-835 1 919-94 Q3(16)57-245 2 916-51 Q2(16)57-422 0 915-03 P i(10)57-605 4 913-50 P 2(10)60-215 1 891-69 Qs(17)60-258 1 891-33 0 ,(1 2 )60-489 0 889-4260-599 0 888-48 Q2(17)61-283 0 882-7861-400 0 881-80 0 ,(8 )61-924 3 877-43 P 2(H )63-737 0 862-31 Qs(18)64-363 0 857-1065-299 0 849-30 0 ,(1 3 )65-449 0 848-0566-403 2 840-12 P 2(12)67-216 —1 833-35 0 ,(9 )67-413 1 831-72 Q 3(19)68-403 0 823-4869-785 0 812-0070-422 0 806-72 0 ,(1 4 )71-028 1 801-69 P 2(13)71-282 0 799-57 Qa(20)72-567 —1 788-9273-189 —1 783-76 0 ,(10 )74-234 —1 775-1175-333 —1 766-01 Q3(21)75-656 —1 763-33 0 ,(15 )75-772 —1 762-38 P a(14)77-984 0 744-0878-198 —1 742-3183-757 —1 696-4585-709 0 680-39

Summary.(1) The X 3400 band attributed by Geuter to a hydride of phosphorus has

been photographed in the second order of the 10-foot grating. Measurements of the wave-lengths have been made with reference to the iron standards recommended by the International Astronomical Union in 1928.

(2) The band has been completely analysed into 27 branches, and is believed to afford the most complete data a t present available for a 3II -> 3£ transition.

(3) The fine structure arising from the 32 level has been resolved and the observed separations compared with Kramers’ theoretical formula. Good agreement is obtained.



354 R,. W . France.

(4) The 3II levels are found to be inverted. An approximate estimation of the electronic energy separations between the three component levels shows that they are not equally spaced but that 2n 2 —2II1 = — 121 cm.-1, while

—2n 0 = — m cm.-1.(5) A complete catalogue of wave-lengths with estimated intensities and

classification is appended.

In conclusion, the author wishes to express his deep gratitude to Prof. A. Fowler for his continued interest and encouragement during the course of this work.

D E SC R IPT IO N O F PLA T E 19.

The P late show s an enlargem ent of the photograph of the X 3400 band of P H taken in th e second order of th e 10-foot grating. The arrangem ent of th e lines into branches is marked below each portion of th e spectrum . The branches are divided in to three sections (a), ( b) and (c), according as th ey belong to the transitions 3II0 -> 3E , 3n j -> 3E and 3I I t -> 3E respectively.

The Absorption Spectrum o f Lithium Vapour.By R. W. F r a n c e , M.Sc., the University, Sheffield.

(Communicated by S, R. Milner, F.R.S.—Received July 23, 1930.)

The absorption spectrum of lithium vapour has been previously studied under low dispersion by several workers. There are two main features of interest in it, the principal series, extending from the first line in the red at 6708 A. to a limit a t 2299 A., and the band structures in the blue-green, 4500- 5500 A. and in the red, 6800-7700 A. The observation of the spectrum is attended by two principal difficulties : first, lithium has a high boiling point, in the neighbourhood of 1400° C. at normal pressure, and it is strongly corrosive at high temperatures ; secondly, the limit of the series has a very low wave-length, this fact rendering it very difficult to use a source not peculiarly rich in ultra-violet light for the transmission of continuous radiation through the vapour.

Bevan, the first worker to publish any data* relating to this spectrum, heated

* ‘ Proc. R oy. Soc.,’ A , vol. 83, p. 43 (1910); A , vol. 85, p. 54 (1911); A , vol. 86, p. 3?0

(1911-12).



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