Bohr's magneton

The Bohr magnet (symbol μ μ B{displaystyle mu _{mathrm {B} },}) is a physical constant related to the magnetic moment of electrons. Specifically, it is the natural unity—and the approximate value— of the intrinsic magnetic moment of an electron. Its value was first calculated in 1911 by the Romanian physicist Ștefan Procopiu, and then in the summer of 1913 by the Danish physicist Niels Bohr.

In the International System of Units, it can be expressed in terms of other elementary constants as:

μ μ B=e 2me{displaystyle mu _{mathrm {B} }={frac {ehbar }{2m_{mathrm {e}}}}}}

Symbol	Name	Value	Unit
μ μ B{displaystyle mu _{mathrm {B}}}}	Bohr Magneton	9.27400915(23)E-24	J/T
e{displaystyle e}	Elementary charge	1.602176634E−19	C
{displaystyle hbar }	Constant of Planck reduced	1.054571817E-34	J s
me{displaystyle m_{e}	Mass at rest of the electron	9.10938291(40)E−31	kg

while in the cegesimal system it is equivalent to:

μ μ B=e 2mec{displaystyle mu _{mathrm {B} }={frac {ehbar }{2m_{mathrm {e} }c}}}}

Symbol	Name	Value	Unit	Ref
μ μ B{displaystyle mu _{mathrm {B}}}}	Bohr Magneton	9.27400915(23)E-21	erg / G
e{displaystyle e}	Elementary charge	4.80320451(10)E−10	Esu
{displaystyle hbar }	Constant of Planck reduced	1.054571817E-27	erg s
me{displaystyle m_{e}	Mass at rest of the electron	9.10938291(40)E−28	g
c{displaystyle c}	Speed of light	29979245800	cm / s

In atomic units it is dimensionless, and its value is simply:

μ μ B=12{displaystyle mu _{mathrm {B} },={frac {1{2}}}}}

Expressed in electronvolts,

μ μ B=5,7883817555(79)× × 10− − 5{displaystyle mu _{mathrm {B} },=5,788,381,755,5(79)times 10^{-5}}}} eV·T^-1

History

The idea of elementary magnets was conjectured by Walter Ritz (1907) and Pierre Weiss. Already before Rutherford's atomic model, many theorists had suggested that the magneton should involve Planck's constant h in its definition. Postulating that the ratio of the kinetic energy of the electron to the orbital frequency should Being equal to h, Richard Gans calculated a value that was twice the Bohr magneton in September 1911. At the first Solvay conference in November of that year, Paul Langevin obtained a submultiple. The Romanian physicist Ştefan Procopiu first obtained its value in 1911; > the value is often referred to as "Bohr–Procopiu magneton" in the Romanian scientific literature. The Bohr magneton is a magnitude of the magnetic dipole moment of an orbiting electron with orbital angular momentum of value ħ. According to Bohr's atomic model, this is the ground state, i.e. the state with the lowest possible energy. In the summer of 1913, this value was obtained naturally by the Danish physicist Niels Bohr as a consequence of his atomic model, and was also published independently by Procopiu, who had published it. obtained using Planck's quantum theory directly. In 1920, Wolfgang Pauli gave the Bohr magneton its current name in a paper comparing it to the magneton that experimental physicists called the Weiss magneton.