Gyromagnetic ratio
The gyromagnetic ratio (also: magnetogyric ratio ) describes the proportionality factor between the angular momentum (or spin) of a particle and the associated magnetic moment
- .
Therefore follows: . The internationally used unit of the gyromagnetic ratio is A · s · kg ^{−1} or s ^{−1} · T ^{−1} . ^{}^{}^{}
The gyromagnetic ratio of a charged particle is the product of its ( dimensionless ) gyromagnetic factor and its magneton , based on the reduced Planck quantum :
With
- the magneton of the particle
- : electric charge
- : Particle mass.
The gyromagnetic ratio can be determined using the Barnett effect and the Einstein-de-Haas effect . In many other experiments, such as B. ferromagnetic resonance or electron spin resonance , the value can deviate significantly from - in this case one speaks of the spectroscopic splitting factor or ratio .
γ _{ℓ} for pure orbital angular momentum of an electron
As explained in the article Magnetic Moment , the following applies to the magnetic moment of the orbital angular momentum of an electron:
- .
With
- the charge of the electron
- its mass.
Hence it follows:
With
- the Bohr magneton . So the g-factor for the orbital movement is
γ _{S} for the spin of a particle
If one considers a particle with spin , then the following applies:
- , respectively
The value of this natural constant is characteristic for every type of particle. According to the current measurement accuracy , it is
- for the free proton :
- for the electron :
the numbers in brackets indicate the estimated standard deviation for the mean value , which corresponds to the last two numbers before the brackets.
The g-factor for spin magnetism for the free electron is almost exactly - with the exception of seven places behind the decimal point - equal to 2. For the free proton, however, the same is by no means true: the magnetic moment of the proton is of the order of the so-called " nuclear magneton " ( that would be the value ), but it is an odd multiple of this value, more precisely: 2.79 times. The neutron also has a magnetic moment, although as a whole it is electrically neutral. Its magnetic moment is −1.91 times that of the nuclear magneton and thus points opposite to that of the proton. It can be explained by the substructure of the neutron.
The ferromagnetic metals iron, cobalt and nickel have electronic g-factors pretty close to 2 (e.g. only about 10% more or less); This means that the magnetism of these systems is predominantly spin magnetism, but with a small orbital component.
Gyromagnetic relationships of atomic nuclei
This ratio can also be measured and specified for cores. Some values are given in the following table.
core |
in 10 ^{7} rad · s ^{−1} · T ^{−1} |
in MHz · T ^{−1} |
---|---|---|
^{1} H. | +26.752 | +42,577 |
^{2} H | +4.1065 | +6.536 |
^{3} He | −20.3789 | −32.434 |
^{7} li | +10.3962 | +16,546 |
^{13} C | +6.7262 | +10.705 |
^{14} N. | +1.9331 | +3.077 |
^{15} N. | −2.7116 | −4.316 |
^{17} O | −3.6264 | −5.772 |
^{19} F | +25.1662 | +40.053 |
^{23} Well | +7.0761 | +11.262 |
^{31} P. | +10.8291 | +17.235 |
^{129} Xe | −7.3997 | −11.777 |
See also
literature
- Horst Stöcker : Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main, 2000, ISBN 3-8171-1628-4 .
- Hermann hook , Hans Christoph Wolf : atomic and quantum physics . 8th edition, Springer-Verlag, Berlin Heidelberg New York, 2004, pp. 194 ff, ISBN 3-540-02621-5 .
Individual evidence
- ↑ Manfred Hesse, Herbert Meier, Bernd Zeeh: Spectroscopic methods in organic chemistry . 7th edition, Georg Thieme Verlag, Stuttgart, 2005, ISBN 3-13-576107-X
- ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed July 16, 2019 . Value for . 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.
- ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed July 16, 2019 . Value for . 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.
- ↑ MA Bernstein, KF King and XJ Zhou: Handbook of MRI Pulse Sequences . Elsevier Academic Press, San Diego 2004, ISBN 0-12-092861-2 , p. 960.
- ↑ RC Weast, MJ Astle (Ed.): Handbook of Chemistry and Physics . CRC Press, Boca Raton 1982, ISBN 0-8493-0463-6 , p. E66.
- ↑ proton gyromagnetic ratio . NIST . 2019.
- ↑ proton gyromagnetic ratio over 2 pi . NIST . 2019.