\sect{Chemical equilibrium A---A+e}

$N$ atoms of type $A$ are placed in a box of volume $V$. 
The system has reached a state of thermal equilibrium ${A \rightleftarrows A^{+} + e^{-}}$.
The mass of the particles is $m_e$, and $m_A$, 
the ionization energy is $\varepsilon$, 
the temperature is $T$, and the gas density is $n=\frac{N}{V}$.

\Dn

(1) Find the percent of ionized atoms, assuming that for ${T \gg T_1}$ the electrons and the atoms form a classical (Boltzmann) gas. 

\Dn

(2) Find the percent of ionized atoms, assuming that for ${T_1 \gg T \gg T_0}$ the electrons form a low temperature Fermi gas, while the atoms still forms a classical Boltzmann gas. 

\Dn

(3) Define the temperatures $T_0$ and $T_1$.


