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Determination of the relative transition-probabilities in the Bergmann-series of CA
O c t o b e r 1937
P h y s i c a IV, n o 9
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 BERGMANN-SERIES OF CA. b y E. K A T Z and L. S. O R N S T E I N (Communication from the Physical Institute of the University of Utrecht)
Abstract. F o l l o w i n g t h e s t a n d a r d p r a c t i c e of t h i s i n s t i t u t e 1) we d e t e r m i n e d 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 Ca-B e r g m a n n - l i n e s ( m ~ F - - 3 s D ) in a t h e r m i c arc, t h e t e m p e r a t u r e of w h i c h was k n o w n f r o m C N - b a n d s or f r o m lines of known transition probabilities. 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 A, d e d u c e d f r o m t h e s e d a t a , are g i v e n in t h e t a b l e below. T h e y s a t i s f y t h e r e l a t i o n A.m4-35 : c o n s t . , e x c e p t t h e f i r s t t r i p l e t , w h i c h h a s a n A - v a l u e 38~ l o w e r t h a n g i v e n b y this relation.
w 1. Apparatus and Method. The spectrum of the light of a Cacontaining arc, produced b y means of a grating-spectrograph, was photographed. On the same plate several spectra of a tungstenb a n d l a m p were photographed, with different lamp currents. The energy-distribution in the continuous spectrum of this lamp as a function of the current was known. This enabled us to express the densities of the spectra on the plate, as determined with the microp h o t o m e t e r of M o 11, in the corresponding intensities 1). This was performed in practice with the apparatus of W o u d a 2), or with a simpler method, described in w3. If the arc is a B o 1 t z m a n n-radiator 3) we have for the relative transition probabilities (t. p.) A'/A of two triplets of the F-D series, the relation : I' A tvt --hcCvt--v)/kT I
--
Av
e
(I'/I stands for the relative intensities of the triplets; 4' and v are their frequencies (cm-1); T is the absolute t e m p e r a t u r e of the arc; - - 757 - Physica IV
48*
758
E. KATZ AND~L.S. ORNSTEIN
h, h, c are the c o n s t a n t of P l a n c k , the constant of B o l t z m a n n and the velocity of light respectively). Thus d e t e r m i n a t i o n of the relative intensities and of the t e m p e r a ture yield the t.p. w 2. The arc. The arc to be used must be a B o 1 t z m a n n-radiator. An arc between two carbon-electrodes satisfies this condition. We used a d.c. arc in air between carbon rods with a core of CaF 2. (Current 5 - - 6 Amp. ; Fieldstrength in the homogeneous column of the arc 27 Volt/cm). The t e m p e r a t u r e in this arc has been d e t e r m i n e d from CN-bands (3884 A) 3). This arc only allowed the d e t e r m i n a t i o n of the relative intensities and t.p. of the first two triplets (m ~ 4 and 5) since the other ones were covered b y the strong bands of CN. The lines showed no self-reversal, which was checked b y measuring the intensity-ratio of the three c o m p o n e n t s of a triplet. According to t h e sum rule of O r n s t e i n - B u r g e r - D o r g e l o this ratio should be 7 : 5 : 3 (see w 4). In order to measure the t.p. of the other triplets, CN m u s t be absent. Also there was a slight continuous background, a p p a r e n t l y due to CaO, which made it difficult to measure the lines accurately. These difficulties disappeared at once, when we used a d.c. arc in Nitrogen of 1 atmosphere, between Ca-metal-electrodes (Current 2.5 A m p . : Fieldstrength in the homogeneous p a r t of the arc 20 Volt/cm). This arc also showed no self-reversal of the lines and yielded the t.p. of the triplets rn = (5), 6, 7, 8. The t e m p e r a t u r e was d e t e r m i n e d from the relative intensities of the triplets m = 4' and 5, using their t.p. as obtained from the first arc. The triplet m = 9 could not be measured, owing to the presence of the Ca + resonnance lines in its neighbourhood; triplets m > 9 possessed intensities too small to be measured. Since the electric fieldstrength in the 2nd arc is low, it is plausible t h a t the mechanism of this discharge is thermic t o o . w 3. Measurement o~ the intensities. The m e a s u r e m e n t of the ,,int e n s i t y a r e a " of a line ( = area of the intensity-wavelength diagram) was p e r f o r m e d with the a p p a r a t u s of W o u d a 2). L a t e r on however we used a different m e t h o d which had the
TRANSITIONPROBABILITIES
IN THE BERGMANN-SERIES
759
O F CA
advantages of taking less time and yet being more accurate. For this purpose we used ,,pre-exposed" plates. These are plates, t h a t have been slightly exposed, before being used to photograph the spectra, and this gives rise to a homogeneous fog of 8--10% ,,density" ( = 1 -- transmission). It appears t h a t spectra on such plates have ,,densities" proportional to the intensities, up to about 40%. F r o m this it follows t h a t one m a y use the areas of the registrations of the microphotometer directly as a measure for the intensities for ,,densities" up to 40% (with a small correction also up to 60%), which causes the advantages mentioned above.
w 4. Results. I st arc: intensity ratio of the triplet components m=4
7 . 0 0 " 4 . 9 8 " 3.00 ~ I % 5 7.02 9 5.02 9 2.98 =L 1 %
temperature derived from CN-bands (3884 A) 2 nd a r c :
4820 ~ ___ 100~
/
intensity ratio of the triplets components m = 4/6.90 9 4.97 "3.06 ~ 2.3% 5 / 7.05 9 5.05 9 2.95 ~ 2.3% /
temperature derived from the first two triplets, using their t.p. as obtained from the I st arc : 5140 ~ ._4:. 350 ~ K TABLE I
transition m3F--33D m=
4
5
6
7
8
w a v e l e n g t h in/~. transition probability A = A • m4.3-~ = m e a n s q u a r e e r r o r of A in %
4581 1.63 680 2.3
4095 1.00 1096 --
3573 0.466 1135 6
3750 0.223 1060 6
3675 O. 129 1096 6
The errors are mean square errors, derived from the spreading of the individual measurements of the intensity ratio's. We estimated the error of the temperature of the 1st arc at about 100 ~ including the error in the transition probabilities of the CN bands used. Indeed the relative values of A are hardly affected by small changes of the temperature of the arc. Physiea IV
48
700
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 B E R G M A N N - S E R I E S OF CA
F r o m the table we see, that, except for the 1st triplet, A • m 4"35 = c o n s t a n t within the experimental error. This result is analogous to those, obtained b y J. K e y and J. H. H e i e r m a n in alkalineseries 5). Finally we t h a n k Dr. H. B r i n k m a n for his helpful advice and Mr. J. H. N. d e J o n g h for his assistance during the experiments. Received July 16, 1937.
LITERATURE 1) L . S . O r n s t e i n , \V. J. H. M o l l , H . C . B u r g e r , Objektive Spektralphotometrie. Braunschweig 1932. 2) J. W o u d a , Z. P h y s i k 7 9 , 5 1 l , 1932. 3) H. B r i n k m a n , Thesis Utrecht 1937. 4) L . S . O r n s t e i n and H. B r i n k m a n , P h y s i c a l , 797, 1934. 5) J. K e y , Thesis Utrecht 1 9 3 7 ; J . H . H e i e r m a n , Thesis Utrecht 1937.
P h y s i c a IV, n o 9
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 BERGMANN-SERIES OF CA. b y E. K A T Z and L. S. O R N S T E I N (Communication from the Physical Institute of the University of Utrecht)
Abstract. F o l l o w i n g t h e s t a n d a r d p r a c t i c e of t h i s i n s t i t u t e 1) we d e t e r m i n e d 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 Ca-B e r g m a n n - l i n e s ( m ~ F - - 3 s D ) in a t h e r m i c arc, t h e t e m p e r a t u r e of w h i c h was k n o w n f r o m C N - b a n d s or f r o m lines of known transition probabilities. 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 A, d e d u c e d f r o m t h e s e d a t a , are g i v e n in t h e t a b l e below. T h e y s a t i s f y t h e r e l a t i o n A.m4-35 : c o n s t . , e x c e p t t h e f i r s t t r i p l e t , w h i c h h a s a n A - v a l u e 38~ l o w e r t h a n g i v e n b y this relation.
w 1. Apparatus and Method. The spectrum of the light of a Cacontaining arc, produced b y means of a grating-spectrograph, was photographed. On the same plate several spectra of a tungstenb a n d l a m p were photographed, with different lamp currents. The energy-distribution in the continuous spectrum of this lamp as a function of the current was known. This enabled us to express the densities of the spectra on the plate, as determined with the microp h o t o m e t e r of M o 11, in the corresponding intensities 1). This was performed in practice with the apparatus of W o u d a 2), or with a simpler method, described in w3. If the arc is a B o 1 t z m a n n-radiator 3) we have for the relative transition probabilities (t. p.) A'/A of two triplets of the F-D series, the relation : I' A tvt --hcCvt--v)/kT I
--
Av
e
(I'/I stands for the relative intensities of the triplets; 4' and v are their frequencies (cm-1); T is the absolute t e m p e r a t u r e of the arc; - - 757 - Physica IV
48*
758
E. KATZ AND~L.S. ORNSTEIN
h, h, c are the c o n s t a n t of P l a n c k , the constant of B o l t z m a n n and the velocity of light respectively). Thus d e t e r m i n a t i o n of the relative intensities and of the t e m p e r a ture yield the t.p. w 2. The arc. The arc to be used must be a B o 1 t z m a n n-radiator. An arc between two carbon-electrodes satisfies this condition. We used a d.c. arc in air between carbon rods with a core of CaF 2. (Current 5 - - 6 Amp. ; Fieldstrength in the homogeneous column of the arc 27 Volt/cm). The t e m p e r a t u r e in this arc has been d e t e r m i n e d from CN-bands (3884 A) 3). This arc only allowed the d e t e r m i n a t i o n of the relative intensities and t.p. of the first two triplets (m ~ 4 and 5) since the other ones were covered b y the strong bands of CN. The lines showed no self-reversal, which was checked b y measuring the intensity-ratio of the three c o m p o n e n t s of a triplet. According to t h e sum rule of O r n s t e i n - B u r g e r - D o r g e l o this ratio should be 7 : 5 : 3 (see w 4). In order to measure the t.p. of the other triplets, CN m u s t be absent. Also there was a slight continuous background, a p p a r e n t l y due to CaO, which made it difficult to measure the lines accurately. These difficulties disappeared at once, when we used a d.c. arc in Nitrogen of 1 atmosphere, between Ca-metal-electrodes (Current 2.5 A m p . : Fieldstrength in the homogeneous p a r t of the arc 20 Volt/cm). This arc also showed no self-reversal of the lines and yielded the t.p. of the triplets rn = (5), 6, 7, 8. The t e m p e r a t u r e was d e t e r m i n e d from the relative intensities of the triplets m = 4' and 5, using their t.p. as obtained from the first arc. The triplet m = 9 could not be measured, owing to the presence of the Ca + resonnance lines in its neighbourhood; triplets m > 9 possessed intensities too small to be measured. Since the electric fieldstrength in the 2nd arc is low, it is plausible t h a t the mechanism of this discharge is thermic t o o . w 3. Measurement o~ the intensities. The m e a s u r e m e n t of the ,,int e n s i t y a r e a " of a line ( = area of the intensity-wavelength diagram) was p e r f o r m e d with the a p p a r a t u s of W o u d a 2). L a t e r on however we used a different m e t h o d which had the
TRANSITIONPROBABILITIES
IN THE BERGMANN-SERIES
759
O F CA
advantages of taking less time and yet being more accurate. For this purpose we used ,,pre-exposed" plates. These are plates, t h a t have been slightly exposed, before being used to photograph the spectra, and this gives rise to a homogeneous fog of 8--10% ,,density" ( = 1 -- transmission). It appears t h a t spectra on such plates have ,,densities" proportional to the intensities, up to about 40%. F r o m this it follows t h a t one m a y use the areas of the registrations of the microphotometer directly as a measure for the intensities for ,,densities" up to 40% (with a small correction also up to 60%), which causes the advantages mentioned above.
w 4. Results. I st arc: intensity ratio of the triplet components m=4
7 . 0 0 " 4 . 9 8 " 3.00 ~ I % 5 7.02 9 5.02 9 2.98 =L 1 %
temperature derived from CN-bands (3884 A) 2 nd a r c :
4820 ~ ___ 100~
/
intensity ratio of the triplets components m = 4/6.90 9 4.97 "3.06 ~ 2.3% 5 / 7.05 9 5.05 9 2.95 ~ 2.3% /
temperature derived from the first two triplets, using their t.p. as obtained from the I st arc : 5140 ~ ._4:. 350 ~ K TABLE I
transition m3F--33D m=
4
5
6
7
8
w a v e l e n g t h in/~. transition probability A = A • m4.3-~ = m e a n s q u a r e e r r o r of A in %
4581 1.63 680 2.3
4095 1.00 1096 --
3573 0.466 1135 6
3750 0.223 1060 6
3675 O. 129 1096 6
The errors are mean square errors, derived from the spreading of the individual measurements of the intensity ratio's. We estimated the error of the temperature of the 1st arc at about 100 ~ including the error in the transition probabilities of the CN bands used. Indeed the relative values of A are hardly affected by small changes of the temperature of the arc. Physiea IV
48
700
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 B E R G M A N N - S E R I E S OF CA
F r o m the table we see, that, except for the 1st triplet, A • m 4"35 = c o n s t a n t within the experimental error. This result is analogous to those, obtained b y J. K e y and J. H. H e i e r m a n in alkalineseries 5). Finally we t h a n k Dr. H. B r i n k m a n for his helpful advice and Mr. J. H. N. d e J o n g h for his assistance during the experiments. Received July 16, 1937.
LITERATURE 1) L . S . O r n s t e i n , \V. J. H. M o l l , H . C . B u r g e r , Objektive Spektralphotometrie. Braunschweig 1932. 2) J. W o u d a , Z. P h y s i k 7 9 , 5 1 l , 1932. 3) H. B r i n k m a n , Thesis Utrecht 1937. 4) L . S . O r n s t e i n and H. B r i n k m a n , P h y s i c a l , 797, 1934. 5) J. K e y , Thesis Utrecht 1 9 3 7 ; J . H . H e i e r m a n , Thesis Utrecht 1937.