# Nuclear magneton

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]

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

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

and in Gaussian CGS units by:

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

where:

e is the elementary charge,
ħ is the reduced Planck constant,
mp is the proton rest mass, and
c is the speed of light

In SI units, its value is approximately:

μN = 5.050783699(31)×10−27 J/T

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

μN = 0.10515446 efm

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 no real Dirac particles, their magnetic moment differ from ${\displaystyle \mu _{\mathrm {N} }}$:

${\displaystyle \mu _{\mathrm {p} }=2{.}79\mu _{\mathrm {N} }}$
${\displaystyle \mu _{\mathrm {n} }=-1{.}91\mu _{\mathrm {N} }}$

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. The Bohr magneton, which is calculated in the same fashion as the nuclear magneton, is larger than μN by a factor equal to the ratio of the proton to electron mass, or about a factor of 1836.

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