Question

Determine the energy of secondary excited state for the particle in one dimensional box

Answer 1

A particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.

Let us consider that the energy of an electron of mass ‘m’ in the nth quantum state in a metal with side ‘L’ is: 

n = 1 for ground state, n = 2 for 1st excited state and n = 3 for second excited state;

En = n² h²/8mL² = n² E₁

E₃ = 3² h²/8mL² = 9E₁

E₃ = 9 x 37.64 eV = 338.76 eV.