LYMAN wavelengths determined from the electron mass

Standard procedure calculates these Lyman wavelengths using the Rydberg constant.
My proposed scheme assumes that the electron mass times Rydeberg equals 1.000000 x 10.
Whereas according to NIST this would only be close at 9.10938188 x 1.09737157 or 9.99637665
This suggested procedure then allows the electron mass to be able to be mutlipled by N 2 over N 2-1

electron mass
N x N -1 911.89065278104 NIST % NCR %
1
4 3 1215.85420370806 1215.673 1.0001491 1215.6737 1.0001485
9 8 1025.87698437867 1025.722 1.0001511 1025.7223 1.0001508
16 15 972.68336296645 972.537 1.0001505 972.5371 1.0001504
25 24 949.88609664692 949.743 1.0001507 949.7431 1.0001506
36 35 937.94467143193 937.803 1.0001511 937.8035 1.0001505
49 48 930.88837471398 930.748 1.0001508 930.7483 1.0001505
64 63 926.36510758709 926.226 1.0001502 926.2257 1.0001505
81 80 923.28928594081 923.1504 1.0001504
100 99 921.10166947580 920.9631 1.0001505
121 120 919.48974155422 919.3515 1.0001504
144 143 918.26751049280 918.1294 1.0001504
169 168 917.31857333331 917.1806 1.0001504
196 195 916.56701510300 916.4292
225 224 915.96159319524 915.8239
256 255 915.46669455665 915.3290
289 288 915.05693976987 914.9193
324 323 914.71384365653 914.5763
361 360 914.42368237210 914.2862
400 399 914.17609301358 914.0386
441 440 913.96313153736 913.8257
484 483 913.77862514705 913.6412
529 528 913.61771841131 913.4803
576 575 913.47654956849 913.3392
625 624 913.35201600665 913.2147
676 675 913.24160189627 913.1043
729 728 913.14324983157 913.0059
784 783 913.05526408728 912.9180
841 840 912.97623689150 912.8389
900 899 912.90499166067 912.7677
961 960 912.84053887769 912.7033
961 960 912.84053887769 912.7033
Interestingly, the electron mass at infinity would therefore ALSO have a wavelength of 911.89065278104181 that is the same as the electron mass of 911.89065278104181. Thus suggesting a direct relationship between mass and wavelengths.


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