The metallic sodium disolves in liquid ammonia to form a deep blue coloured solution. The deep blue colour is due to formation of: 

The alkali metals dissolve in liquid ammonia without evolution of hydrogen. The metal loses electrons and combine with ammonia molecule. 
$$\begin{gathered} \mathbf{M}⟶{\mathbf{M}}^{+}\text{(in liquid ammonia) }+{\mathrm{e}}^{-}\text{(ammoniated) } \\ \mathrm{M}+(\mathrm{x}+\mathrm{y}){\mathrm{NH}}_3\to {\left[\mathrm{M}{\left({\mathrm{NH}}_3\right)}_{\mathrm{x}}\right]}^{+}+{\mathrm{e}}^{-}{\left({\mathrm{NH}}_3\right)}_{\mathrm{y}} \\ \mathrm{Solvated} \mathrm{electron} \end{gathered}$$
It is ammoniated electron which is responsible for color.