A particle in a 3-dimensional quadratic box with box length L hasan energy given byh²E = (n+n+n). The degeneracies of the first, second, and8mL²third level area.e.1, 2, 31, 3, 3b. 1, 3, 1c. 3, 3, 3d. 1, 2, 2

Degeneracy: Degeneracy can be defined as the number of states having the same energy.Formula for the energy of the particle:The energy of a particle trapped in three dimensional box having side length is given by the expression, (1)where is Planck's constant, is the mass of particle, is the energy of the state, and are positive integers.The possible values of integers () for the first energy level are (1, 1, 1). Hence the possible state for the first energy level is (1, 1, 1). There are no other possible states for the first energy level as per equation (1). Hence the degeneracy of the first energy level is one.The possible values of integers for the second energy level are (2, 1, 1), (1, 2, 1), and (1, 1, 2). This is because according to equation (1), they will give the same energy. The energy of second level is greater than the energy of first level which can be observed from equation (1). Hence there are three states corresponding to second energy level. Hence the degeneracy of the second energy level is three.The possible values of integers for the third energy level are (2, 2, 1), (2, 1, 2), and (1, 2, 2). This is because according to equation (1), they will give the same energy. The energy of third level is greater than the energy of second level which can be observed from equation (2). Hence there are three states corresponding to third energy level. Hence the degeneracy of the third energy level is three.From the previous step, the degeneracy of the first, second, and third energy levels are 1, 3, and 3 respectively. Only option (e) matches the result obtained using concepts. Hence option (e) is correct while other options are incorrect.Option (e)The first, second, and third energy levels have degeneracy 1, 3, and 3 respectively.

Answered: A particle in a 3-dimensional quadratic…

A particle in a 3-dimensional quadratic box with box length L has an energy given by (n+n+n2). The degeneracies of the first, second, and E 8mL2 third level are a. 1, 2, 3 e. 1, 3, 3 b. 1, 3, 1 b. 1, 3, 1 c. 3, 3, 3 d. 1, 2, 2