Nuclear magneton

The nuclear magneton (symbol μ_N), is a physical constant of magnetic moment, defined in SI units by:

${\displaystyle \mu _{\text{N}}={{e\hbar } \over {2m_{\text{p}}}}}$

The value of nuclear magneton

System of units	Value	Unit
SI	5.050783699(31)×10^−27	J·T^−1
CGS	5.050783699(31)×10^−24	Erg·G^−1
eV	3.1524512550(15)×10^−8	eV·T^−1
MHz/T (per h)	7.622593285(47)	MHz/T[1]

and in Gaussian CGS units by:

${\displaystyle \mu _{\text{N}}={{e\hbar } \over {2m_{\text{p}}c}}}$

where:

e is the elementary charge,

ħ is the reduced Planck constant,

m_p is the proton rest mass, and

c is the speed of light

In SI units, its value is approximately:

μ_N = 5.050783699(31)×10⁻²⁷ J/T

In Gaussian CGS units, its value can be given in convenient units as

μ_N = 0.10515446 e⋅fm

The nuclear magneton is the natural unit for expressing magnetic dipole moments of heavy particles such as nucleons and atomic nuclei.

Due to the fact that neutrons and protons consist of quarks and thus are not really Dirac particles, their magnetic moments differ from μ_N:

${\displaystyle \mu _{\text{p}}=2{.}793\mu _{\text{N}}}$

${\displaystyle \mu _{\text{n}}=-1{.}913\mu _{\text{N}}}$

The magnetic dipole moment of the electron, which is much larger as a consequence of much larger charge-to-mass ratio, is usually expressed in units of the Bohr magneton, which is calculated in the same fashion using the electron mass. The result is larger than μ_N by a factor equal to the ratio of the proton to electron mass, or about a factor of 1836.

See also

• Neutron magnetic moment
• Proton magnetic moment

References

1. "nuclear magneton in MHz/T: ${\displaystyle \mu _{\rm {N}}/h}$". NIST. 2014. CODATA recommended values

External links

• "Nuclear magneton". NIST. 2014. CODATA recommended value.
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