Ratio of Proton Moment to Nuclear Magneton
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Theorem
The ratio of the proton moment to the nuclear magneton is given by:
| \(\ds \dfrac {\mu_{\mathrm p} } {\mu_{\mathrm N} }\) | \(=\) | \(\ds 2 \cdotp 79284 \, 73446 \, 3(82)\) |
Proof
We have:
| \(\ds \mu_{\mathrm N}\) | \(=\) | \(\ds 5 \cdotp 05078 \, 3699 \, (31) \times 10^{-27} \, \mathrm {J \, T^{-1} }\) | Definition of Nuclear Magneton | |||||||||||
| \(\ds \mu_{\mathrm p}\) | \(=\) | \(\ds 1 \cdotp 41060 \, 67973 \, 6 \, (60) \times 10^{-26} \, \mathrm {J \, T^{-1} }\) | Definition of Proton Moment | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \dfrac {\mu_{\mathrm p} } {\mu_{\mathrm N} }\) | \(=\) | \(\ds 2 \cdotp 79284 \, 73446 \, 3 \, (82)\) | by calculation |
$\blacksquare$
Sources
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $2$. Physical Constants and Conversion Factors: Table $2.3$ Adjusted Values of Constants
- which gives the mantissa as $2 \cdotp 792 \, 782$, with an uncertainty of $\pm 17$ corresponding to the $2$ least significant figures