detailed solutions/equations for both*** Part 1 Five electrons are in a two-dime

Question

detailed solutions/equations for both***

Part 1

Five electrons are in a two-dimensional square potential energy well with sides of length L.The potential energy is infinite at the sides and zero inside. The single particle energies are given by (h2/8mL2)(n2x +n2y), where nx and ny are integers. In units of (h2/8mL2) the energy of the ground state of the system

Part2

Electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by (h2/8mL2)(n2x + n2y), where nx and ny are integers. At most the number of electrons that can have energy 8(h2/8mL2) is:

Explanation / Answer

Part 1:

    The energy of particle in two dimensional square potential well

                           E = (h2/ 8mL2) ( nx2 + ny2)

Five electrons are inside the well.

            here every state has occupied by 2 electons

               electron occupied the state, 1x - 2 electron,   1y - 2 electron

                                                         2x - 1 electron

                                 E = (h2/ 8mL2)( 12 + 12 + 22)

                                     E = 6 (h2 / 8mL2)

                 The energy of ground state of the five electron system is 6 (h2/ 8mL2)

Part 2:

                  Energy of the system   E= 8 (h2/8mL2)

                     here n2 = 8

   Possible states are nx = 2, ny= 2

   n2 = 22 + 22 =8

State equavalent to the energy E= 8 (h2/ 8mL2) is   Ex,y = E2,2

          Every state is occupied by two electrons 2x = 2 electron,

                                                                       2y=2 electron

                   The number of electron occupied the state E2,2 = 4 electrons

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.