  The mass-radius relations for white dwarf stars are investigated by solving
the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for
hydrostatic equilibrium assuming the electron gas to be non-interacting. We
find that the Newtonian limiting mass of $1.4562M_\odot$ is modified to
$1.4166M_\odot$ in the general relativistic case for $^4_2$He (and $^{12}_{\
6}$C) white dwarf stars. Using the same general relativistic treatment, the
critical mass for $^{56}_{26}$Fe white dwarf is obtained as $1.2230M_\odot$. In
addition, departure from the ideal degenerate equation of state (EoS) is
accounted for by considering Salpeter's EoS along with the TOV equations
yielding slightly lower values for the critical masses, namely
$1.4081M_{\odot}$ for $^4_2$He, $1.3916M_{\odot}$ for $^{12}_{\ 6}$C and
$1.1565M_{\odot}$ for $^{56}_{26}$Fe white dwarfs. We also compare the critical
densities for gravitational instability with the neutronization threshold
densities to find that $^4_2$He and $^{12}_{\ 6}$C white dwarf stars are stable
against neutronization with the critical values of $1.4081M_\odot$ and
$1.3916M_{\odot}$, respectively. However the critical masses for $^{16}_{\
8}$O, $^{20}_{10}$Ne, $^{24}_{12}$Mg, $^{28}_{14}$Si, $^{32}_{16}$S and
$^{56}_{26}$Fe white dwarf stars are lower due to neutronization. Corresponding
to their central densities for neutronization thresholds, we obtain their
maximum stable masses due to neutronization by solving the TOV equation coupled
with the Salpeter EoS.
