Nuclear magneton

Physical constant
Surname	Nuclear magneton
Formula symbol	${\displaystyle \mu _{\mathrm {K} },\,\mu _{\mathrm {N} }}$
Size type	Magnetic moment
value
SI	5.050 783 7461 (15)e-27 ${\displaystyle \textstyle {\frac {\mathrm {J} }{\mathrm {T} }}}$
Uncertainty  (rel.)	3.1e-10
Relation to other constants
${\displaystyle \mu _{\mathrm {N} }={\frac {e}{2m_{\mathrm {p} }}}\,\hbar }$
Sources and Notes
Source SI value: CODATA 2018 ( direct link )

The nuclear magneton ( symbol or with N for nucleon ) is usually used in nuclear and particle physics as a unit for magnetic moments . It is defined as the magnitude of the magnetic moment of a Dirac particle with the charge and mass of the proton : ${\displaystyle \mu _{\mathrm {K} }}$ ${\displaystyle \mu _{\mathrm {N} }}$

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

With

${\displaystyle e}$: elementary electric charge

${\displaystyle \hbar }$: reduced Planck's quantum of action

${\displaystyle m_{\mathrm {p} }}$: Proton mass.

According to the current measurement accuracy , it has the value:

${\displaystyle {\begin{aligned}\mu _{\mathrm {N} }&=3{,}152\,451\,258\,44(96)\cdot 10^{-8}\ \mathrm {eV/T} \\&=5{,}050\,783\,7461(15)\cdot 10^{-27}\ \mathrm {J/T} ,\end{aligned}}}$

The numbers in brackets denote the uncertainty in the last digits of the value; this uncertainty is given as the estimated standard deviation of the specified numerical value from the actual value; there are

${\displaystyle \mathrm {eV} }$or for the energy units electron volt or joule ${\displaystyle \mathrm {J} }$

${\displaystyle \mathrm {T} }$for the unit Tesla of the magnetic flux density .

The measured magnetic moments of protons and neutrons are:

${\displaystyle {\begin{aligned}\mu _{\mathrm {p} }&=2{,}7928\,\mu _{\mathrm {N} }\\\mu _{\mathrm {n} }&=-1{,}9130\,\mu _{\mathrm {N} },\end{aligned}}}$

If they were point-like particles, one would expect and . This clear discrepancy was one of the earliest indications that protons and neutrons are composite particles (made up of quarks , as we know today). ${\displaystyle \mu _{\mathrm {p} }=1\,\mu _{\mathrm {N} }}$ ${\displaystyle \mu _{\mathrm {n} }=0\,\mu _{\mathrm {N} }}$

See also

• Bohr's magneton
• Gyromagnetic ratio

Individual evidence

1. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed July 20, 2019 .  Value for in the unit electron volts per Tesla ${\displaystyle \mu _{\mathrm {N} }}$
2. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed July 20, 2019 .  Value for in the unit Joule per Tesla ${\displaystyle \mu _{\mathrm {N} }}$