In the ATM origin of charge I showed the following equation to derive the value of q.
and X=(mass of proton-mass of electron)/mass of neutron
The top equation can be rearranged to define the Rydberg constant as shown below, the defining the Rydberg constant in terms of the proton electron and neutron and the Planck constant.
Rnc is the neutron comptom wavelength and Rec is the electron comptom wavelength.
this number is within the accuracy of the known rest masses of the proton neutron and electron and the Planck constant.