Atomic mass constant

Electron mass measurement

In practice, the atomic mass constant is determined from the electron rest massm_e and the electron relative atomic massA_r(e) (that is, the mass of electron divided by the atomic mass constant). The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants. $${\displaystyle {\begin{aligned}m_{\text{u}}&={\frac {m_{\text{e}}}{A_{\text{r}}({\text{e}})}}={\frac {2R_{\infty }h}{A_{\text{r}}({\text{e}})c\alpha ^{2}}}={\frac {M_{\text{u}}}{N_{\text{A}}}},\\[1ex]N_{\text{A}}&={\frac {M_{\text{u}}A_{\text{r}}({\text{e}})}{m_{\text{e}}}}={\frac {M_{\text{u}}A_{\text{r}}({\text{e}})c\alpha ^{2}}{2R_{\infty }h}},\end{aligned}}}$$ where c is the speed of light, h is the Planck constant, α is the fine-structure constant, and R_∞ is the Rydberg constant.