Reduced Compton Wavelength of Proton

Theorem

The Compton wavelength of the proton is:

\(\ds \lambdabar_{\mathrm p}\)

\(\approx\)

\(\ds 2 \cdotp 10308 \, 9103 \times 10^{-16} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 10308 \, 9103 \times 10^{-14} \, \mathrm {cm}\)

Symbol

$\lambdabar_{\mathrm p}$

The symbol for the reduced Compton wavelength of the proton is $\lambdabar_{\mathrm p}$.

The $\LaTeX$ code for \(\lambdabar_{\mathrm p}\) is \lambdabar_{\mathrm p} .

Proof

By definition, the reduced Compton wavelength $\lambdabar_{\mathrm p}$ of a proton is given as:

$\lambdabar_{\mathrm p} = \dfrac {\lambda_{\mathrm p} } {2 \pi}$

where $\lambda_{\mathrm p}$ denotes the Compton wavelength of the proton.

Then we have:

\(\ds \lambda_{\mathrm p}\)

\(\approx\)

\(\ds 1 \cdotp 32140 \, 98553 \, 9(40) \times 10^{-15} \, \mathrm m\)

Compton Wavelength of Proton

\(\ds \leadsto \ \ \)

\(\ds \lambdabar_{\mathrm p}\)

\(\approx\)

\(\ds \dfrac {1 \cdotp 32140 \, 98553 \, 9(40) \times 10^{-15} } {2 \pi} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 10308 \, 9103 \times 10^{-16} \, \mathrm m\)

by calculation

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 10308 \, 9103 \times 10^{-14} \, \mathrm {cm}\)

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 $3 \cdotp 861 \, 692$ with an uncertainty of $\pm 12$ corresponding to the $2$ least significant figures