**Mass fractions**

The mass fraction of H, He and the metals is a quick way to specify the chemical composition of the stellar plasma. The mass fraction of hydrogen is defined as ratio of the mass of hydrogen particles and the total mass of all particles (in a given volume): $$ X = \frac{M_\mathrm{H}}{M}= \frac{\rho_\mathrm{H}}{\rho}, $$ where $\rho_\mathrm{H}$ and $\rho$ are the respective (mass) densities. The hydrogen mass density is equal to the hydrogen number density ($n_\mathrm{H}$) times the mass of one hydrogen particle $m_{\mathrm{H}} = A_{\mathrm{H}}\,m_{\mathscr{A}}$, thus: $$ X = \frac{M_\mathrm{H}}{M}= \frac{n_\mathrm{H}\,m_{\mathrm{H}}}{\rho}= \frac{n_\mathrm{H}\,A_{\mathrm{H}}\,m_{\mathscr{A}}}{\rho}. $$ Similar to that, for helium and the metals we define: $$ Y = \frac{M_\mathrm{He}}{M}= \frac{n_\mathrm{He}\,m_{\mathrm{He}}}{\rho}= \frac{n_\mathrm{He}\,A_{\mathrm{He}}\,m_{\mathscr{A}}}{\rho}, $$ $$ Z = \frac{M_\mathrm{metals}}{M}= \frac{n_\mathrm{metals}\,m_{\mathrm{metals}}}{\rho} = \frac{\sum_{i=3} n_\mathrm{i}\,A_{\mathrm{i}}\,m_{\mathscr{A}}}{\rho},. $$