Proton to Electron Mass Ratio

Physical Law

The ratio of the mass of the proton to the mass of an electron is given by:

$\dfrac {m_{\mathrm p} } {m_{\mathrm e} } \approx 1 836 \cdotp 15267 \,343$

This sequence is A005601 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Demonstration

From Mass of Proton, we have:

$m_{\mathrm p} \approx 1.67262 \, 19236 \, 9(51) \times 10^{-27}$ kilograms

From Mass of Electron, we have:

$m_{\mathrm e} \approx 9.10938 \, 370 \, 15(28) \times 10^{-31}$ kilograms

Hence:

$\dfrac {m_{\mathrm p} } {m_{\mathrm e} } \approx 1 836 \cdotp 15267 \,343$

$\blacksquare$

Sources

• 1958: C.A. Coulson: Electricity (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: Preliminary Survey: $\S 1$. Electrostatics
• 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $3.$ Physical Constants