An electron is in an infinitely deep one$-$dimensional potential well with a width $\backslash$ell$,$ and the energy of the ground state is $4\mathrm{.}0$ eV$.$

a$)$ What is the width of the well? $(2$ points$)$

b$)$ What is the smallest possible momentum of the electron? $(2$ points$)$

c$)$ What is the maximum possible wavelength of a photon that the system can emit? $(4$ points$)$