Particle in a box — UPSC CSE 1993 Physics PYQ

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.