[UPSC CSE 1993] Schrodinger’s Wave equation and applications (Q233, 20M)

Using de Broglie's relation, deduce an expression for energy values of a particle enclosed in a one-dimensional box. 'Free electrons' in a long-chain molecule may be treated as particles in a one-dimensional box. From a long-chain molecule of length 60\text{ \AA} deduce the lowest three energy state values in eV units.