Relativistic Irregular and Regular Doublet Laws Extract from D.Sc. Madras Thesis (yrs.1922-1924) by Prof. K. R Rao, D.Sc. (Madras) D.Sc. (London)

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Vol. 2014, Issue No.3, Dated: 17th March 2014 : Time 13h50m P.M.

Relativistic Irregular and Regular Doublet Laws

Extract from D.Sc. Madras Thesis (yrs.1922-1924)

By Prof. K. R Rao D.Sc. (Madras) D.Sc. (London)

Page 74

    The Primary Series :- The first Principal, Sharp and

Diffuse series fall in the extreme ultraviolet and

attempts are here made to fix these, if possible, only by

extrapolation and then seek for confirmation by correlating

the members of the spectra of related elements i.e. InII etc.

The method led to the suggestion of the probable, chief triplet

of the Sharp Series. But in spite of such confirmation, it

may be stated that this cannot be considered as final

and requires experimental confirmation.

          The usual Rydberg relation and formula applied to

the above mentioned two triplets lead to the position λ 1020

as the approximate position of the triplet  1 ³ p _{0,1 2} – 1 ³ s ₁ with

separation 1 ³ p ₁ – 1 ³ p ₂  =  3150. A more correct idea of the

separation is perhaps obtained from the relation that

in the similar spectra of elements of the same vertical group

of the periodic table, Δν (1 ³ p ₁ – 1 ³ p ₂  ) a value of about 4500.

          The only available values of λ wave length of spark

lines of Tin in the required region are those of Lang ⁵⁴ A

very careful search is made for a possible p triplet among

these lines of λ below 1400 A. U. having in view the

relative outer and magnitudes of the intensities and the

probable ratio of the intervals between the lines in the

triplet. This search revealed the following----

λ  (vac)                 Int               ν                 Δν

                     1251.3                   (60)         79917

                                                                                           4138

                     1189.7                   (40)          84055

                                                                                           2286     

                     1158.2                   (60)          86431                      

  

Page 75

          Evidence for the possibility of this to be regarded  as

the member 1³p – 1³ s of Sn III is now sought by searching

for the corresponding triplets in the spectrum of In II with

the aid of the Relativistic Irregular and Regular Doublet

Laws and also in the spectrum of Ga II, --- the spectra of

which are found to resemble very closely the corresponding

Spectra of Indium.

          The method, as shown below, is that adopted by

Millikan & Bowen ⁵⁵ in the identification of lines of CIII.

                            

Formula on p gives -----

ν’/R={(n₂² – n₁²)Z² – 2(n²₂ σ ₁  - n₁²σ₂ )Z + n²₂ σ₁² - n²₁ σ₂²}/( n²₁ n²₂)

In the case under consideration, the line 1³p – 1³s₁,

or “Bohr notation ( 5³p – 6³ s₁) is due to an electron jump

between two orbits of different total quantum numbers i.e.

n₂   is different from  n₁.

                             Hence transposing—

ν’-  R (Z²) (n₂² – n₁²) / (n²₁ n²₂)   = c Z + D

 or

ν’  -  R (Z- A)² (n₂² – n₁²) / (n²₁ n²₂)   = c’ Z + D’

The whole expression on the left side varies linearly

with the atomic number Z for any particular set of

values of n ₂ ,  n₁ ,  σ_{1  ,} σ₂ .

Here n 2- 6 & n1 =5

∴    R  (n₂² – n₁²) / (n²₁ n²₂)   =    R   (6² – 5²) / (6² 5²)=1340.5

                                                R being 109,737. 

Page 76

The first column in the table below gives the value

of  n of Cd I and the above value tentatively supposed

to be that of Sn III

                             Putting A= 47

                   For Cd I ==è n’ =  n -1340.5 x 1²

                                                = 19656.8-1340.5

                                                = 18316.3.

                   For Sn III =è n’ =  79917 -1340.5 x 3²

                                                 = 67852

Hence the table  è

Atomic Number       Z	Element	n   53p2-63s1	n’ = n - 1340.5(Z-A)2	Diff
48 49 50	Cd  I In II Sn III	19656.8 [48093]   79917.	18316 [42731]   67852	24415 25121

Interpolation gives a value for In II of  n’ equal to

 About 43300 or  n = 48662.

Regular Doublet law =è

           Dn =  5³p₁ - 5³p₂  =    .0234 (Z-s) ⁴

Atomic Number       Z	Element	D n	--------------- 4 Ö D n /0.0234	s
48 49 50	Cd  I In II Sn III	1171   [2481]    4138	14.96    [18.05]       20.5	33.04  [30.95]   29.5

          Interpolation gives about 31 for the screening

constant ‘s’ for In II. This leads to    D n = .0234(49-31) ⁴

                                                                      = 2457

Page 77 

The following triplet in the spectrum of Indium

is found to be exactly in agreement with prediction.

The respective values, adopting this triplet, are shown in

the above tables enclosed in brackets. It is seen that the

Relativistic Laws are exactly satisfied.

          For purpose of comparison the values of wave-

lengths and intensities of different observers are

given below.

Saunders56 l  I . A .	Weinberg l vac   Int	Eder & Valenta l(Rao)  Int	Carroll l vac   Int	n  (vac)	D n
2079.28  (7) 1977.44  (5)      ---	2079.6 (5) 1977.8 (6) 1936.5 (4)	2078.8  (8) 1976.8  (7) 1935.9  (5)	2079.3(4) 1977.3(3) 1936.8(3)	48093 505574 51632	2481   1058

                                                                  

The wave-numbers are calculated from the recent

measures of carroll. The exact coincidence of observed

and calculated values of the triplet perhaps lends good

support to the correctness of the identification.

          Further support is given by the discovery of the

corresponding triplet, shown below, in the spark

Spectrum of Gallium, which is very prominently

seen in the beautiful spectrograms accompanying

Carroll’s paper and agrees excellently with that of

In II as regards position, frequency interval etc.— 

Page 78

The triplet 1³p_{2, 1 ,0} – 1³s₁ of Ga II è

Weinberg  l (vac)        Int	Carroll  l (vac)        Int	n  (vac)	D n
1845.0         (8) 1813.8         (9) 1799.1         (6)	1845.28      (9) 1813.91      (9) 1799.31      (7)	54201      55133      55583	932          450

There is a Displacement of the member towards the

region of shorter wave-lengths as we pass from In II to

Ga II. Values of Dn  / Z ² for elements of the same chemical

Group are =è

Atomic    Number         Z	Element	Dn   2 3 p 1-  2 3 p 2	Dn  / Z 2
13          31          49	Al II    Ga II    In  II	125.5      932.0      2481	.743         .97         1.034

For comparison a similar table for the group of

spectra Al III etc. is also added                        

Element	Dn	Dn  / Z 2
Al III    Ga III    In  III	238      1714      4345	1.41        1.70        1.81

Term Values:- Term values characteristic of the

spectrum of Sn III cannot be determined as the

series has not yet been completely determined and

Page 79

The first member of the diffuse series which is expected

to occur in the ultra-violet below  l 1000 A.U is not

known.

ADDENDUM

I have recently published a booklet in December 2013, on "Anti-Photon" giving the possibility of collapse of Einstein’s Theory of Relativity, giving way to a possibility of Anti-Photons being released from the Earth’s interior and, spurting up to interact with the Earth’s bound atmosphere contents.

Prof K R Rao has foreseen the possibility of

 Relativistic Irregular and Regular Doublet Laws.