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Determination of the relative transition-probabilities in the spectrum of cadmium
P h y s i c a V, n o 3
M a a r t 1938
D E T E R M I N A T I O N OF T H E R E L A T I V E T R A N S I T I O N - P R O B A B I L I T I E S IN T H E S P E C T R U M OF CADMIUM by L. S. ORNSTEIN, J. P. A. VAN HENGSTUM and H. BRINKMAN (Communication from the Physical Institute of the University of Utrecht)
Summary I n d.c. a n d a.c. c a r b o n a r c s i n a i r b e t w e e n Cd-filled e l e c t r o d e s , t h e r e l a t i v e i n t e n s i t i e s of t h e m a i n C d - l i n e s h a v e b e e n m e a s u r e d p h o t o graphically. Assuming that these arcs are B o 1 t z m a n n-radiators a f t e r t h e t h e o r y of O r n s t e i n and Brinkman, the relative t r a n s i t i o n - p r o b a b i l i t i e s (t.p.) of t h e C d - l i n e s a r e d e r i v e d f r o m t h e i n t e n s i t i e s a n d t h e s p e t r o s c o p i c a l l y m e a s u r e d t e m p e r a t u r e of t h e g a s i n t h e c o l u m n of t h e arcs. T h e e x c e l l e n t a g r e e m e n t b e t w e e n t h e t . p . o b t a i n e d w i t h d.c. a r c s of d i f f e r e n t t e m p e r a t u r e s a n d i n d i f f e r e n t p h a s e s of a.c. arcs, a g a i n w i t h d i f f e r e n t t e m p e r a t u r e s , s h o w s t h e e x i s t e n c e of t h e a s s u m e d t h e r m i c e x c i t a t i o n m e c h a n i s m in t h e c o l u m n of t h e s e arcs. The measured relative values o / t h e E i n s t e i n transition probabilities /or Cd are shown i n Table I V and i n fig. 1. The sum rule for intensities has been checked for some multiplets. In the m sS--5 sp triplets small deviations seem to exist; within the m aDS 'P multiplets the agreement with the theoretically predicted intensities is good.
§1. Method and apparatus. As a
light-source
we used
an arc
between electrodes of carbon with a core of Cd-salt, burning in air at atmospheric pressure. At first we had bored a small hole in one of the carbon electrodes and filled this with Cd-salt. In this case, however, the spectrum was disturbed by a strong continuous background and by the CN-bands. A carbon arc with a large hole in one of the electrodes (diameter 10 mm in carbonelectrode of 12 mm diam.) filled with a mixture of CdO and an other chemical compound, for example ZnO or AgC1, proved more suitable for 145 Physica V
10
146 L. S. ORNSTEIN, J. P. A. VAN HENGSTUM AND H. BRINKMAN
our purpose; with these substances, the intensity of the continuous background and of the CN-bands is greatly reduced. The salt used for the mixture must possess about the same excitation-voltage as the Cd-salt, because otherwise the temperature of the gas in the arc falls to such an extent, that the Cd-lines become too weak. We have checked the influence of self-absorption b y putting several percentages of CdO in the mixture and measuring the ratio of the components of the first triplet (63S1--53p2,1,0). From these measurements it appea~ed that for percentages of CdO, less than 10S/o, the ratio of the intensities of the triplet lines was constant. The actual intensity measurements were carried out with only 1s/o of CdO. An image of the arc was formed b y means of anachromatic quartzfluorite lens on the slit of a H i 1 g e r E 1 spectograph and the spectrum was then photographed. On th~ same plate we photographed the spectra of a Tungsten-bancUamp, run with different lamp currents. The energy-distribution in the continuous spectrum of this .lamp as a function of the current was known 1) and the intensities of the various Cd spectral lines were determined according to the wellknown photographic-photometric method ~). From these intensities the relative transition-probabilities (t.p.) can be calculated b y means of the formula: I t
A ~ g' v ~ e--lVlhT
I
A g v e-~lkT
if the mechanism of the arc discharge is a thermic one 8). In this formula I is the measured intensity of the line, A the t.p., g the statistical weight, ~ the frequency, E the energy of the initial level, k the constant of B o 1 t z m a n n, T the absolute temperature. In order to apply this formula, we had to determine the tempera-" ture in the arc. This was done from the relative intensities of the vibration bands of the CN bandgroups ~ 3883 A 3) and ~ 4216 A 4). To fix the t.p. with higher accuracy, we measured the intensities of the lines at different temperatures, in a direct current (d.c.) as well as in a alternating current (a.c.) arc. The agreement between the values found in this w a y for the t.p. is a confirmation of the hypothesis, that in the arc with d.c. as well as in the different phases of the arc with a.c., the mechanism of the discharge is a thermic one.
RELATIVE TRANSITION-PROBABILITIES OF CADMIUM
147
§ 2. Direct current arc. In this arc, we were able to vary the temperature b y changing the composition of the mixture of the salt. In this way, we obtained a temperature of more than 5500°K with a CdOZnO-filling; with a CdO-AgCl-filling temperatures between 5000 ° and 5500 °, while b y adding a little NaC1 (5%) to the mixture of ZnO and CdO a further drop of the temperature was obtained to about 4500°K. For these d.c. exposures, only the anode (the lower electrode) was filled and we used a current strength of 5 Amp. while the field strength in the column of the arc was about 20 Volt/cm. Alternating current arc. Here we obtained different temperatures b y means of observing the arc stroboscopically i n . different phases 5). It must be noted, however, that the difference of thetemperature between the various phases of the arc, the electrodes being filled with the CdO mixture, is smaller than in the a.c. arc between two homogeneous carbon electrodes 5). In the carbon arc with a Cd-filling, the difference of the temperature between the arc in the phase 90 ° (maximum temperature) and in the phase 45 ° is only 300°; and between the phases 45 ° and 30 ° 600 °. For 25 ° and smaller phases the intensity of the Cd-lines and the temperature fall strongly. In order to observe the Cd-spectrum also in the a.c. arc at widely different temperatures (see table II), it is necessary to alter the composition of the salt-mixture in the electrodes at the same time as the phases. The disadvantage of the a.c. arc is, that the times of exposure are about a factor 60 longer than for the d.c. arc. This consequence of the stroboscopical method of observation gives rise to difficulties as the arc does not burn steadily all the time. However, we can-overcome this difficulty for the greater part, b y adding a little NaC1 to the filling, since with this mixture the arc burns much more steadily. § 3. Checking o/the sum-rule. For this purpose, we have measured the values of A.g for the following multiplets:
63S1 - - 53P2'1'° } 73SI - - 53P2,1,o
and
5 aD3'2'I - - 5 3P2'1'° } 63D3,2,l - - 5 3~D2,1,0 "
It appears (see tables IA, IB, IC, ID) that the 3D 3 p multiplets give results which are in accordance with theory, whereas the 3S--3P
148
L. S. O R N S T E I N ,
J . P. A. V A N H E N G S T U M
A N D H. B R I N K M A N
triplets give deviations, which are not neutralized b y applying the ~*-correction e). In the tables IC and ID, the numbers placed in parentheses, are the theoretical values of A.g for the 3 / : ) - 3p multiplets. In order to give some idea of the accuracy of the results, we have added in table IV the number of exposures, used for the determination of the various intensity ratios of the triplet components. TABLE
TABLE IB
IA.
T r i p l e t 7 aS, -- 5 3Pa,t,o
T r i p l e t 6 aS, - - 5 aPa,,,o
6 'S,-
5
aP a
,,
--
5 spt
,,
--
5
'Po
).
I/'~
I/'•*
5085,9 4799,9 4678,2
5 4,1 1,2
5 3,46 0,94
J
,~
7 3S,- 5 sPa 3252,5 ,, - - 5 aPt -3133,2 - - 5 3Po 3080,9
II'J
I/v*
5 3,25 0,81
5 2,90 0,69
T A B L E IC M u l t i p l e t 5 aDa,,,,, - - 5 5 5
aP a
5
apt
5
3Pa
100 (I00)
7
5 3Dr
5 3D2
aD a
16,4 52,6
(7)
(17,9) (53,6)
4,83
aPa~,,o
(5)
1,5 (1,2) 17,4 (17,9) 23,8 (23,8) 2,99 (3)
5
(5)
2,97 (3) 1,01 (I)
TABLE ID M u l t i p l e t 6 3D3,a, l - - 5 aPa,,,o 6 5 aPl 3 aP t 5 spa
aD a
lOOUoo)
6 3D2 17,6") 52,0
6 3D 1
(I 7,9) (53,6)
1,5 (1,2) 16,8 (17,9)
23,0 (23,8) 7
(7)
4,87
(5)
2,89
5 (5) 2,92 (3) 0,98 (I)
(3)
The mean deviation (i.e. the arithmetic sum of the deviations from the average, divided b y the number of measurements) was about *) This line 6 3D2 - - 5 aP 2 (X = 2981, 3 A) was d i s t u r b e d b y a Fe line 0, = 2981,45 A). As we could not o b t a i n a n arc, e n t i r e l y free from iron, we also took e x p o s u r e s of a few s p e c t r a w i t h o u t Cd and d e t e r m i n e d the i n t e n s i t y r a t i o of the d i s t u r b i n g Fe-line to one of the n e i g h b o u r i n g Fe-lines. This r a t i o t u r n e d o u t to be c o n s t a n t for the various exposures, so t h a t we could a f t e r w a r d s d e t e r m i n e the i n t e n s i t y of the d i s t u r b i n g Fe-line, b y m e a s u r i n g the n e i g h b o u r i n g Fe-line a n d a p p l y i n g the k n o w n ratio.
RELATIVE
TRANSITION-PROBABILITIES
149
OF CADMIUM
4% to 5%, except for the two very weak linles X = 3614.4 A and X = 2981.9 A and for the lines ~ = 2881.2 A and k = 2880.7 A, which are strongly disturbed by a Si-line, so that it was necessary to analyse the line pattern. The average deviation of these four lines was about 6% to 7%. However, we see, that the probable error is very small, owing to the very great number of measurements.
§ 4. Determination o/the relative t.p. o~ the various multiplets. We have invariably compared the strongest component of one multiplet with the strongest component of the other multiplet; the following lines are, therefore,
used: 6 aS 1 - -
5 3P2;
X -~ 5085.9
A
5aD 3-
,,
;
k---- 3 6 1 0 . 5 A
73S 1 --
,,
;
X=3252.5A
63D 3-
,,
;
~,-= 2980.6A.
In the computation of the relative t.p., the temperature plays an important part. We have therefore inserted table II, showing the considerable difference of intensity between lines with an energy difference of one volt between the initial levels. These intensity ratios and temperatures are, all of them the mean values of about eight exposures, taken on one and the same plate under the same conditions. This applies also to table I l i A and n l B , which give a general survey of the experimental A.g values of these multiplets, derived respectively from the exposures of d.c. and a.c. arcs, while table I I I C shows the average results. In the first two tables the temperatures, at which the intensities are measured, have been added. In the last column of these tables, the averages are inserted from which the good agreement appears between d.c. arc and a.c. arc results. T A B L E II
I/v
l'/v"
X = 5085,9
X = 3610,5
T
Boltzmannfactor
A.g X 5085,9
A.g X 3610,5
arc (
216,6 122,3 107,0
100 100 100
4400 ° 5450 ° 6100 °
13,75 8,33 6,63
15,78 14,70 16,12
100 100 100
2;2{'
143.0 I06,0 88,2
I00 I00 I00
5200 ° 5850 ° 6450 °
9,22
15,51 15,02 14,70
100 I00 I00
!
d. c.~ i
7,05
6,00
M a a r t 1938
D E T E R M I N A T I O N OF T H E R E L A T I V E T R A N S I T I O N - P R O B A B I L I T I E S IN T H E S P E C T R U M OF CADMIUM by L. S. ORNSTEIN, J. P. A. VAN HENGSTUM and H. BRINKMAN (Communication from the Physical Institute of the University of Utrecht)
Summary I n d.c. a n d a.c. c a r b o n a r c s i n a i r b e t w e e n Cd-filled e l e c t r o d e s , t h e r e l a t i v e i n t e n s i t i e s of t h e m a i n C d - l i n e s h a v e b e e n m e a s u r e d p h o t o graphically. Assuming that these arcs are B o 1 t z m a n n-radiators a f t e r t h e t h e o r y of O r n s t e i n and Brinkman, the relative t r a n s i t i o n - p r o b a b i l i t i e s (t.p.) of t h e C d - l i n e s a r e d e r i v e d f r o m t h e i n t e n s i t i e s a n d t h e s p e t r o s c o p i c a l l y m e a s u r e d t e m p e r a t u r e of t h e g a s i n t h e c o l u m n of t h e arcs. T h e e x c e l l e n t a g r e e m e n t b e t w e e n t h e t . p . o b t a i n e d w i t h d.c. a r c s of d i f f e r e n t t e m p e r a t u r e s a n d i n d i f f e r e n t p h a s e s of a.c. arcs, a g a i n w i t h d i f f e r e n t t e m p e r a t u r e s , s h o w s t h e e x i s t e n c e of t h e a s s u m e d t h e r m i c e x c i t a t i o n m e c h a n i s m in t h e c o l u m n of t h e s e arcs. The measured relative values o / t h e E i n s t e i n transition probabilities /or Cd are shown i n Table I V and i n fig. 1. The sum rule for intensities has been checked for some multiplets. In the m sS--5 sp triplets small deviations seem to exist; within the m aDS 'P multiplets the agreement with the theoretically predicted intensities is good.
§1. Method and apparatus. As a
light-source
we used
an arc
between electrodes of carbon with a core of Cd-salt, burning in air at atmospheric pressure. At first we had bored a small hole in one of the carbon electrodes and filled this with Cd-salt. In this case, however, the spectrum was disturbed by a strong continuous background and by the CN-bands. A carbon arc with a large hole in one of the electrodes (diameter 10 mm in carbonelectrode of 12 mm diam.) filled with a mixture of CdO and an other chemical compound, for example ZnO or AgC1, proved more suitable for 145 Physica V
10
146 L. S. ORNSTEIN, J. P. A. VAN HENGSTUM AND H. BRINKMAN
our purpose; with these substances, the intensity of the continuous background and of the CN-bands is greatly reduced. The salt used for the mixture must possess about the same excitation-voltage as the Cd-salt, because otherwise the temperature of the gas in the arc falls to such an extent, that the Cd-lines become too weak. We have checked the influence of self-absorption b y putting several percentages of CdO in the mixture and measuring the ratio of the components of the first triplet (63S1--53p2,1,0). From these measurements it appea~ed that for percentages of CdO, less than 10S/o, the ratio of the intensities of the triplet lines was constant. The actual intensity measurements were carried out with only 1s/o of CdO. An image of the arc was formed b y means of anachromatic quartzfluorite lens on the slit of a H i 1 g e r E 1 spectograph and the spectrum was then photographed. On th~ same plate we photographed the spectra of a Tungsten-bancUamp, run with different lamp currents. The energy-distribution in the continuous spectrum of this .lamp as a function of the current was known 1) and the intensities of the various Cd spectral lines were determined according to the wellknown photographic-photometric method ~). From these intensities the relative transition-probabilities (t.p.) can be calculated b y means of the formula: I t
A ~ g' v ~ e--lVlhT
I
A g v e-~lkT
if the mechanism of the arc discharge is a thermic one 8). In this formula I is the measured intensity of the line, A the t.p., g the statistical weight, ~ the frequency, E the energy of the initial level, k the constant of B o 1 t z m a n n, T the absolute temperature. In order to apply this formula, we had to determine the tempera-" ture in the arc. This was done from the relative intensities of the vibration bands of the CN bandgroups ~ 3883 A 3) and ~ 4216 A 4). To fix the t.p. with higher accuracy, we measured the intensities of the lines at different temperatures, in a direct current (d.c.) as well as in a alternating current (a.c.) arc. The agreement between the values found in this w a y for the t.p. is a confirmation of the hypothesis, that in the arc with d.c. as well as in the different phases of the arc with a.c., the mechanism of the discharge is a thermic one.
RELATIVE TRANSITION-PROBABILITIES OF CADMIUM
147
§ 2. Direct current arc. In this arc, we were able to vary the temperature b y changing the composition of the mixture of the salt. In this way, we obtained a temperature of more than 5500°K with a CdOZnO-filling; with a CdO-AgCl-filling temperatures between 5000 ° and 5500 °, while b y adding a little NaC1 (5%) to the mixture of ZnO and CdO a further drop of the temperature was obtained to about 4500°K. For these d.c. exposures, only the anode (the lower electrode) was filled and we used a current strength of 5 Amp. while the field strength in the column of the arc was about 20 Volt/cm. Alternating current arc. Here we obtained different temperatures b y means of observing the arc stroboscopically i n . different phases 5). It must be noted, however, that the difference of thetemperature between the various phases of the arc, the electrodes being filled with the CdO mixture, is smaller than in the a.c. arc between two homogeneous carbon electrodes 5). In the carbon arc with a Cd-filling, the difference of the temperature between the arc in the phase 90 ° (maximum temperature) and in the phase 45 ° is only 300°; and between the phases 45 ° and 30 ° 600 °. For 25 ° and smaller phases the intensity of the Cd-lines and the temperature fall strongly. In order to observe the Cd-spectrum also in the a.c. arc at widely different temperatures (see table II), it is necessary to alter the composition of the salt-mixture in the electrodes at the same time as the phases. The disadvantage of the a.c. arc is, that the times of exposure are about a factor 60 longer than for the d.c. arc. This consequence of the stroboscopical method of observation gives rise to difficulties as the arc does not burn steadily all the time. However, we can-overcome this difficulty for the greater part, b y adding a little NaC1 to the filling, since with this mixture the arc burns much more steadily. § 3. Checking o/the sum-rule. For this purpose, we have measured the values of A.g for the following multiplets:
63S1 - - 53P2'1'° } 73SI - - 53P2,1,o
and
5 aD3'2'I - - 5 3P2'1'° } 63D3,2,l - - 5 3~D2,1,0 "
It appears (see tables IA, IB, IC, ID) that the 3D 3 p multiplets give results which are in accordance with theory, whereas the 3S--3P
148
L. S. O R N S T E I N ,
J . P. A. V A N H E N G S T U M
A N D H. B R I N K M A N
triplets give deviations, which are not neutralized b y applying the ~*-correction e). In the tables IC and ID, the numbers placed in parentheses, are the theoretical values of A.g for the 3 / : ) - 3p multiplets. In order to give some idea of the accuracy of the results, we have added in table IV the number of exposures, used for the determination of the various intensity ratios of the triplet components. TABLE
TABLE IB
IA.
T r i p l e t 7 aS, -- 5 3Pa,t,o
T r i p l e t 6 aS, - - 5 aPa,,,o
6 'S,-
5
aP a
,,
--
5 spt
,,
--
5
'Po
).
I/'~
I/'•*
5085,9 4799,9 4678,2
5 4,1 1,2
5 3,46 0,94
J
,~
7 3S,- 5 sPa 3252,5 ,, - - 5 aPt -3133,2 - - 5 3Po 3080,9
II'J
I/v*
5 3,25 0,81
5 2,90 0,69
T A B L E IC M u l t i p l e t 5 aDa,,,,, - - 5 5 5
aP a
5
apt
5
3Pa
100 (I00)
7
5 3Dr
5 3D2
aD a
16,4 52,6
(7)
(17,9) (53,6)
4,83
aPa~,,o
(5)
1,5 (1,2) 17,4 (17,9) 23,8 (23,8) 2,99 (3)
5
(5)
2,97 (3) 1,01 (I)
TABLE ID M u l t i p l e t 6 3D3,a, l - - 5 aPa,,,o 6 5 aPl 3 aP t 5 spa
aD a
lOOUoo)
6 3D2 17,6") 52,0
6 3D 1
(I 7,9) (53,6)
1,5 (1,2) 16,8 (17,9)
23,0 (23,8) 7
(7)
4,87
(5)
2,89
5 (5) 2,92 (3) 0,98 (I)
(3)
The mean deviation (i.e. the arithmetic sum of the deviations from the average, divided b y the number of measurements) was about *) This line 6 3D2 - - 5 aP 2 (X = 2981, 3 A) was d i s t u r b e d b y a Fe line 0, = 2981,45 A). As we could not o b t a i n a n arc, e n t i r e l y free from iron, we also took e x p o s u r e s of a few s p e c t r a w i t h o u t Cd and d e t e r m i n e d the i n t e n s i t y r a t i o of the d i s t u r b i n g Fe-line to one of the n e i g h b o u r i n g Fe-lines. This r a t i o t u r n e d o u t to be c o n s t a n t for the various exposures, so t h a t we could a f t e r w a r d s d e t e r m i n e the i n t e n s i t y of the d i s t u r b i n g Fe-line, b y m e a s u r i n g the n e i g h b o u r i n g Fe-line a n d a p p l y i n g the k n o w n ratio.
RELATIVE
TRANSITION-PROBABILITIES
149
OF CADMIUM
4% to 5%, except for the two very weak linles X = 3614.4 A and X = 2981.9 A and for the lines ~ = 2881.2 A and k = 2880.7 A, which are strongly disturbed by a Si-line, so that it was necessary to analyse the line pattern. The average deviation of these four lines was about 6% to 7%. However, we see, that the probable error is very small, owing to the very great number of measurements.
§ 4. Determination o/the relative t.p. o~ the various multiplets. We have invariably compared the strongest component of one multiplet with the strongest component of the other multiplet; the following lines are, therefore,
used: 6 aS 1 - -
5 3P2;
X -~ 5085.9
A
5aD 3-
,,
;
k---- 3 6 1 0 . 5 A
73S 1 --
,,
;
X=3252.5A
63D 3-
,,
;
~,-= 2980.6A.
In the computation of the relative t.p., the temperature plays an important part. We have therefore inserted table II, showing the considerable difference of intensity between lines with an energy difference of one volt between the initial levels. These intensity ratios and temperatures are, all of them the mean values of about eight exposures, taken on one and the same plate under the same conditions. This applies also to table I l i A and n l B , which give a general survey of the experimental A.g values of these multiplets, derived respectively from the exposures of d.c. and a.c. arcs, while table I I I C shows the average results. In the first two tables the temperatures, at which the intensities are measured, have been added. In the last column of these tables, the averages are inserted from which the good agreement appears between d.c. arc and a.c. arc results. T A B L E II
I/v
l'/v"
X = 5085,9
X = 3610,5
T
Boltzmannfactor
A.g X 5085,9
A.g X 3610,5
arc (
216,6 122,3 107,0
100 100 100
4400 ° 5450 ° 6100 °
13,75 8,33 6,63
15,78 14,70 16,12
100 100 100
2;2{'
143.0 I06,0 88,2
I00 I00 I00
5200 ° 5850 ° 6450 °
9,22
15,51 15,02 14,70
100 I00 I00
!
d. c.~ i
7,05
6,00