L. Pauling & E.B. Wilson Jr. explained Bohr magneton in their 1935 classic "Introduction to Quantum Mechanics". This note is to understand it in SI units with current constant values. And it's just for me to have some idea about the magnitude of the constants. "goldbook" at iupac.org is recommended to find out the exact constant values including Bohr magneton.
Based on the book, magnetic moment of 1 Bohr magneton is he/(4πmc).
where at that time,
Planck constant h=6.547e-27 erg sec (1 erg =1e-7 Joules,)
electron charge e=4.770e-10 abs e.s.u. (absolute electrostatic unit, or statcoulomb)
electron mass m=9.035e-28 g
speed or velocity of light c=2.99796e10 cm /sec
It was given that Magnetic moment of 1 Bohr magneton μ0 = 0.9175e-20 erg/gauss
Nowadays,
h=6.626e-34 Js
e=4.8025e-10 abs e.s.u., or
e=1.602e-19 C (note if using 1.6e-19C, speed of light should be removed in the equation. Note that e in unit C is smaller by a factor of c, the speed of light, compared to e in e.s.u.)
m=9.109e-31 kg
c=2.99792e8 m/s
1 Bohr magneton μ0 = 9.274e-24 J/T
To roughly check the result, 1 erg = 1e-7 J, 1 gauss = 1e-4 T. Therefore, the two values are reasonably close to each other.
On iupac goldbook website, Bohr magneton μB = 9.2740154e-24 J/T
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