Compton Wavelength of Electron

Theorem

The Compton wavelength of the electron is:

\(\ds \lambda_\E\)

\(\approx\)

\(\ds 2 \cdotp 42631 \, 02386 \, 7(73) \times 10^{-12} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 42631 \, 02386 \, 7(73) \times 10^{-10} \, \mathrm {cm}\)

Symbol

$\lambda_\E$

The symbol for the Compton wavelength of the electron is $\lambda_\E$.

The $\LaTeX$ code for \(\lambda_\E\) is \lambda_\E .

Proof

By definition, the Compton wavelength $\lambda_\E$ of an electron is given as:

$\lambda_\E = \dfrac h {m_\E c}$

where:

$m_\E$ denotes the mass of the electron

$h$ denotes Planck's constant

$c$ denotes the speed of light.

Then we have:

\(\ds h\)

\(=\)

\(\ds 6 \cdotp 62607 \, 015 \times 10^{-34} \, \mathrm {J \, s}\)

that is: joule seconds

\(\quad\) Definition of Planck's Constant

\(\ds m_\E\)

\(\approx\)

\(\ds 9 \cdotp 10938 \, 37015 \, (28) \times 10^{-31} \, \mathrm {kg}\)

that is: kilograms

\(\quad\) Mass of Electron

\(\ds c\)

\(=\)

\(\ds 299 \, 792 \, 458 \, \mathrm {m \, s^{-1} }\)

that is: metres per second

\(\quad\) Definition of Speed of Light

\(\ds \leadsto \ \ \)

\(\ds \lambda_\E\)

\(\approx\)

\(\ds \dfrac {6 \cdotp 62607 \, 015 \times 10^{-34} } {9 \cdotp 10938 \, 37015 \, (28) \times 10^{-31} \times 299 \, 792 \, 458} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 42631 \, 02386 \, 7 (73) \times 10^{-12} \, \mathrm m\)

\(\quad\) by calculation

\(\ds \)

\(\approx\)

\(\ds 2 \cdotp 42631 \, 02386 \, 7 (73) \times 10^{-10} \, \mathrm {cm}\)

\(\quad\) 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 $2 \cdotp 426 \, 309 \, 6$ with an uncertainty of $\pm 74$ corresponding to the $2$ least significant figures