APPENDIX A

Emission Spectra for the First 7 Orbital Shells, (Down to the 3rd), of Hydrogen, (as so far Developed).

This Appendix presents calculated emission/absorption spectra for the first 7 Ž 3 orbit shells of hydrogen. They include the effects of relativistic mass correction, magnetic dipole coupling and the Lamb Shift. The spectra are calculated using the formula

l_{( n )( m )} =

( E_{or( m )} -E_{or( n )} )

(A.1)

together with the Selection Rules.

For spectra in which the wavelength is greater than 2000Å, (A.1) is divided by P_air , the refractive index of air, to enable a direct comparison of the results with those in [5].

In (A.1), E_{or(# )} is given by (4.2) within which n_j is given by [9], Eq.(3.20). R_hy is determined from the generalised relationship

R_hy =

c R_Ľ { Z m_p +( J - Z )m_N }

{ Z m_p +( J - Z )m_N +m_e }

(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	[11]
c	Velocity of Light in Vacuum	2.99792458E+10	cm/sec	[11]
R_hy	Rydberg's Constant for Hydrogen	See (A.2)	sec^-1
R_Ľ	Rydberg's Constant for Infinite Nuclear Mass	1.09737316E+5	cm^-1	[11]
Z	Atomic Number	1 for Hydrogen
J	Mass Number	1 for Hydrogen
m_p	Proton Mass	1.67262171E-24	g sec²/cm	[11]
m_N	Neutron Mass	1.6749278E-24	g sec²/cm	[11]
m_e	Electron Mass	9.10913826E-28	g sec²/cm	[11]
e	Electron/Proton Charge	-/+ 4.8032044E-10	esu	See Note 1
g_p	Proton magnetic moment constant of proportionality	2.79275	-	[2]
d_p	Proton spin dipole magnetisation constant of proportionality	3.3558912	-	[9]
P_air	Refractive Index of Air	See Table A.2	-	Calculated from [12]

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 P_air used, are shown in the following table, as calculated from [12].

Wavelength	P_air
3889	1.000283373820
3970	1.000282912237
4101	1.000282223812
4340	1.000281143049
4861	1.000279342657
6562	1.000276235841
9545	1.000274299185
10049	1.000274132698
10938	1.000273891534
12817	1.000273537699
18751	1.000273036604
19445	1.000273006377
21654	1.000272927044
26251	1.000272823218
37395	1.000272707134
40510	1.000272691823
46525	1.000272669382
74577	1.000272628864
75003	1.000272628349
123682	1.000272605744
190568	1.000272607289

Table A.2 - Pair vs Wavelength.

The only apparent anomaly in this table is that the last two entries appear reversed. This will accentuate any differences to [5] with respect to the emission spectra at the wavelengths concerned.

The calculated orbital energy levels and transition emission spectra are shown below in Table A.3 expressed as wavelengths in Ångstroms.

Orbital Energy - E_OR

From
Ż

To Ž

n*_f

0.5

1.5

0.5

1.5

2.5

ergs

cm^-1

n*_f

s(+)

p(+)

p(-)

s(+)

p(+)

p(-)

d(+)

d(-)

-2.178709E-11

0.0000

0.5

s(+)

N.P.

-5.446796E-12

82258.916

0.5

s(+)

N.P.

-5.446731E-12

82259.247

1.5

p(+)

1215.6683

N.P.

-5.446803E-12

82258.882

1.5

p(-)

1215.6737

N.P.

-2.420791E-12

97492.1739

0.5

s(+)

N.P.

6,562.9089

6,562.7532

N.P.

-2.420772E-12

97492.2699

1.5

p(+)

1025.7219

6,562.7270

N.P.

-2.420793E-12

97492.1643

1.5

p(-)

1025.7230

6,562.7725

N.P.

-2.420765E-12

97492.3035

2.5

d(+)

N.P.

6,562.8530

N.P.

-2.420772E-12

97492.2692

2.5

d(-)

N.P.

6,562.8678

6,562.7121

N.P.

-1.361692E-12

102823.802

0.5

s(+)

N.P.

4,861.3747

4,861.2893

N.P.

18,751.2061

18,750.8348

N.P.

-1.361684E-12

102823.841

1.5

p(+)

972.5367

4,861.2883

N.P.

18,750.7294

N.P.

18,751.1854

18,751.0645

-1.361692E-12

102823.798

1.5

p(-)

972.5371

4,861.2986

N.P.

18,750.8827

N.P.

18,751.2179

-1.361681E-12

102823.855

2.5

d(+)

N.P.

4,861.3621

N.P.

18,751.0184

N.P.

-1.361684E-12

102823.841

2.5

d(-)

N.P.

4,861.3654

4,861.2800

N.P.

18,751.0678

18,750.6966

N.P.

-1.361680E-12

102823.862

3.5

f(+)

N.P.

18,751.1119

N.P.

-1.361681E-12

102823.855

3.5

f(-)

N.P.

18,751.1360

18,751.0151

-8.714811E-13

105291.578

0.5

s(+)

N.P.

4,340.4998

4,340.4317

N.P.

12,818.1376

12,817.9641

N.P.

-8.714772E-13

105291.598

1.5

p(+)

949.7430

4,340.4347

N.P.

12,817.9476

N.P.

12,818.1607

12,818.1042

-8.714815E-13

105291.576

1.5

p(-)

949.7432

4,340.4388

N.P.

12,817.9833

N.P.

12,818.1399

-8.714758E-13

105291.605

2.5

d(+)

N.P.

4,340.4948

N.P.

12,818.0940

N.P.

-8.714772E-13

105291.598

2.5

d(-)

N.P.

4,340.4962

4,340.4281

N.P.

12,818.1055

12,817.9320

N.P.

-8.714751E-13

105291.608

3.5

f(+)

N.P.

12,818.1436

N.P.

-8.714758E-13

105291.605

3.5

f(-)

N.P.

12,818.1492

12,818.0927

-8.714747E-13

105291.610

4.5

g(+)

N.P.

-8.714751E-13

105291.608

4.5

g(-)

N.P.

-6.051944E-13

106632.096

0.5

s(+)

N.P.

4,101.7660

4,101.7052

N.P.

10,938.1262

10,937.9999

N.P.

-6.051922E-13

106632.107

1.5

p(+)

937.8034

4,101.7092

N.P.

10,937.9982

N.P.

10,938.1534

10,938.1123

-6.051946E-13

106632.095

1.5

p(-)

937.8035

4,101.7113

N.P.

10,938.0128

N.P.

10,938.1268

-6.051914E-13

106632.111

2.5

d(+)

N.P.

4,101.7635

N.P.

10,938.1085

N.P.

-6.051922E-13

106632.107

2.5

d(-)

N.P.

4,101.7641

4,101.7033

N.P.

10,938.1132

10,937.9868

N.P.

-6.051910E-13

106632.113

3.5

f(+)

N.P.

10,938.1464

N.P.

-6.051914E-13

106632.111

3.5

f(-)

N.P.

10,938.1487

10,938.1076

-6.051908E-13

106632.114

4.5

g(+)

N.P.

-6.051910E-13

106632.113

4.5

g(-)

N.P.

-6.051907E-13

106632.115

5.5

h(+)

N.P.

-6.051908E-13

106632.114

5.5

h(-)

N.P.

-4.446321E-13

107440.385

0.5

s(+)

N.P.

3,970.1008

3,970.0438

N.P.

10,049.3961

10,049.2895

N.P.

-4.446308E-13

107440.391

1.5

p(+)

930.7483

3,970.0483

N.P.

10,049.2925

N.P.

10,049.4235

10,049.3888

-4.446323E-13

107440.384

1.5

p(-)

930.7483

3,970.0495

N.P.

10,049.3000

N.P.

10,049.3962

-4.446303E-13

107440.394

2.5

d(+)

N.P.

3,970.0994

N.P.

10,049.3871

N.P.

-4.446308E-13

107440.391

2.5

d(-)

N.P.

3,970.0997

3,970.0428

N.P.

10,049.3895

10,049.2829

N.P.

-4.446301E-13

107440.395

3.5

f(+)

N.P.

10,049.4200

N.P.

-4.446303E-13

107440.394

3.5

f(-)

N.P.

10,049.4211

10,049.3864

-4.446300E-13

107440.395

4.5

g(+)

N.P.

-4.446301E-13

107440.395

4.5

g(-)

N.P.

-4.446299E-13

107440.396

5.5

h(+)

N.P.

-4.446300E-13

107440.396

5.5

h(-)

N.P.

-4.446298E-13

107440.396

6.5

i(+)

N.P.

-4.446299E-13

107440.396

6.5

i(-)

N.P.

N.P. = Not Permitted by the Selection Rules.

Table A.3 - Line Spectra for the First Seven to Three Orbital Shells of Hydrogen

The spreadsheet that produced Table A.3 covers a wider orbit shell range and is available for download as:-

Hydrogen Spectra

This spreadsheet is cell locked but contains a small area highlighted at the bottom of the 1^st sheet wherein a spot check of any desired transition can be performed via the input of just six parameters in six unlocked cells. Ionisation levels can also be checked here.

Two other sheets are incorporated in this spreadsheet

(i) the relevant orbital energy levels and spectral wavelengths from [5], and

(ii) the differences in the values in (i) and the top sheet.

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

P5 Version 1.1.1
Ó P.G.Bass, April 2008

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