Appendix A

The Hyperfine Addition to the Hydrogen Fine Structure Emission Spectra for Orbit Shells 1 to 3 to Orbit Shells 1 and 2.

This Appendix presents calculated emission/absorption spectra for the first 3 ® 2 orbit shells of hydrogen. They include the effects of relativistic mass correction, magnetic dipole coupling, the Lamb Shift and hyperfine variations. The spectra are calculated using the formula


l( n )( m ) = hc
( Eor( m ) -Eor( n ) )
(A.1)
together with the Selection Rules.

For spectra in which the wavelength is greater than 2000Å, (A.1) is divided by Pair, the refractive index of air. In (A.1), Eor(# ) is given by (2.7) within which nj is given by [1], Eq.(3.20), ensp and pnsp= ± 1/ 2 , and nf * is increased by unity in the ground state orbitals when ensp = - 1/ 2. Rhy is determined from the generalised relationship


Rhy = cR¥ { Zmp +( J-Z )mN }
{ Zmp +( J-Z )mN +me }
(A.2)

In this and the other relationships referred to, the values of the parameters used are as shown in the following Table A.1.


Parameter Name Value Units Ref.
h   Planck's Constant   6.6260693E-27   erg secs [7]
c   Velocity of Light in Vacuum 2.99792458E+10   cm/sec [7]
Rhy   Rydberg's Constant for Hydrogen   See (A.2)   sec-1 -
R¥   Rydberg's Constant for Infinite Nuclear Mass   1.09737316E+5   cm-1 [7]
Z   Atomic Number   1 for Hydrogen - -
J   Mass Number   1 for Hydrogen - -
mp   Proton Mass   1.67262171E-24   g sec2/cm [7]
mN   Neutron Mass   1.6749278E-24   g sec2/cm [7]
me   Electron Mass   9.10913826E-28   g sec2/cm [7]
e   Electron/Proton Charge   -/+ 4.8032044E-10   esu See Note 1
gp   Proton magnetic moment constant of proportionality   2.79275 - [4]
dp   Proton spin dipole magnetisation constant of proportionality   3.3548035 - [1]
Pair   Refractive Index of Air   See Table A.2 - Calculated from [8]

Table A1 - Parameter Values.
Note 1:- Calculated from e = 1.60217653E-20 abcoulombs x c.
Also the following factors have been used to convert energy from ergs to cm-1.

Joules = 1E-7 ergs;              eV = 6.24150948E+18 Joules              cm-1 = 8.065541E+3 eV

The values of Pair used, are shown in the following table, as calculated from [8].

Wavelength Pair
38891.000283373820
39701.000282912237
41011.000282223812
43401.000281143049
48611.000279342657
65621.000276235841
95451.000274299185
100491.000274132698
109381.000273891534
128171.000273537699
187511.000273036604
194451.000273006377
216541.000272927044
262511.000272823218
373951.000272707134
405101.000272691823
465251.000272669382
745771.000272628864
750031.000272628349
1236821.000272605744
1905681.000272607289
> 2000001.000272526299

Table A.2 - Pair vs Wavelength.

The only apparent anomaly in this table is that the values for l = 123,682Å and 190,568Å appear reversed.

The calculated orbital energy levels and transition emission spectra are shown below in Table A.3 expressed as wavelengths in Ångstroms for inter-shell transitions, and cm for intra-shell transitions.

Orbital Energy - EOR                           To ®
      From   ¯		 n 1 2 3
n*f 0.5 1.5 1.5 0.5 1.5 1.5 0.5 0.5 1.5 1.5 1.5 1.5 0.5 0.5 2.5 2.5 1.5 1.5 2.5
ergs cm-1 n n*f ensp pnsp nf Term s(+) sh1(-) sh2(-) sh3(+) p(-) ph(-) s(+) sh(+) p(+) ph(+) p(-) ph(-) s(+) sh(+) d(-) dh(-) p(+) ph1(+) d(+)
-2.1787E-11 0.0000 1 0.5 0.5 0.5 1.5 s(+)                                      
-2.1787E-11 0.0275 1.5 -0.5 -0.5 0.5 sh1(-) N.P.                                    
-2.1787E-11 0.0474 1.5 -0.5 0.5 1.5 sh2(-) 21.1061 N.P.                                  
-2.1787E-11 0.0596 0.5 0.5 -0.5 0.5 sh(+) N.P. N.P. N.P.                                
-5.4468E-12 82258.881 2 1.5 -0.5 -0.5 0.5 p(-) 1215.6737 N.P. N.P. 1215.6746     D.Z.                        
-5.4468E-12 82258.884 1.5 -0.5 0.5 1.5 ph(-) 1215.6736 N.P. N.P. N.P. N.P.     D.Z.                      
-5.4468E-12 82258.917 0.5 0.5 0.5 1.5 s(+) N.P. 1215.6736 1215.6739 N.P. D.Z. N.P.                          
-5.4468E-12 82258.924 0.5 0.5 -0.5 0.5 sh(+) N.P. 1215.6735 1215.6737 N.P. N.P. D.Z. N.P.                        
-5.4467E-12 82259.247 1.5 0.5 0.5 2.5 p(+) 1215.6683 N.P. N.P. N.P. N.P. N.P. N.P. N.P.                      
-5.4467E-12 82259.248 1.5 0.5 -0.5 1.5 ph(+) 1215.6683 N.P. N.P. 1215.6691 N.P. N.P. N.P. N.P. N.P.                    
-2.4208E-12 97492.165 3 1.5 -0.5 -0.5 0.5 p(-) 1025.7230 N.P. N.P. 1025.7236 N.P. N.P. 6562.773 6562.776 N.P. N.P.     D.Z.            
-2.4208E-12 97492.165 1.5 -0.5 0.5 1.5 ph(-) 1025.7230 N.P. N.P. N.P. N.P. N.P. 6562.772 N.P. N.P. N.P. N.P.     D.Z.          
-2.4208E-12 97492.174 0.5 0.5 0.5 1.5 s(+) N.P. 1025.7232 1025.7234 N.P. 6562.753 6562.754 N.P. N.P. 6562.911 N.P. D.Z. N.P.              
-2.4208E-12 97492.177 0.5 0.5 -0.5 0.5 sh(+) 1025.7232 1025.7234 N.P. N.P. 6562.752 6562.753 N.P. N.P. N.P. 6562.910 N.P. D.Z. N.P.            
-2.4208E-12 97492.270 2.5 -0.5 -0.5 1.5 d(-) N.P. 1025.7222 1025.7224 N.P. 6562.712 6562.713 N.P. N.P. 6562.870 6562.870 N.P. N.P. N.P. N.P.     D.Z.    
-2.4208E-12 97492.271 2.5 -0.5 0.5 2.5 dh(-) N.P. N.P. 1025.7224 N.P. N.P. 6562.713 N.P. N.P. 6562.869 N.P. N.P. N.P. N.P. N.P. N.P.     D.Z.  
-2.4208E-12 97492.272 1.5 0.5 0.5 2.5 p(+) 1025.7219 N.P. N.P. N.P. N.P. N.P. 6562.726 N.P. N.P. N.P. N.P. N.P. N.P. N.P. D.Z. N.P.      
-2.4208E-12 97492.272 1.5 0.5 -0.5 1.5 ph(+) 1025.7219 N.P. N.P. N.P. N.P. N.P. 6562.726 6562.730 N.P. N.P. N.P. N.P. N.P. N.P. N.P. D.Z. N.P.    
-2.4208E-12 97492.306 2.5 0.5 0.5 3.5 d(+) N.P. N.P. N.P. 1025.7225 N.P. N.P. N.P. N.P. 6562.854 N.P. N.P. N.P. N.P. N.P. N.P. N.P. N.P. N.P.  
-2.4208E-12 97492.306 2.5 0.5 -0.5 2.5 dh(+) N.P. N.P. N.P. N.P. N.P. N.P. N.P. N.P. 6562.854 6562.854 N.P. N.P. N.P. N.P. N.P. N.P. N.P. N.P. N.P.

Table A.3 - Hyperfine and Normal Spectral Wavelengths for Transitions from Cells 1 to 3, to Cells 1 & 2.


The spreadsheet that produced Table A.3 is available for download as:-

Hydrogen Spectra
Three other sheets are incorporated in this spreadsheet.
(i) The revised hydrogen fine structure orbital energy levels and emission spectra and other data, (See Appendix B).

(ii) The relevant orbital energy levels and spectral wavelengths from [6].

(iii) The differences in the values in (i) and (ii).

Note that this spreadsheet is a working document that has "evolved" as the development in this series of papers has progressed. Presentation has not therefore been aesthetically optimised.



P6 Version 1.0.0
Ó P.G.Bass, August 2007
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