Question

The degeneracy of a system of NA identical molecules A in a three-dimensional box has the form g = V^ (NA) f(EA,NA). If we add NB more molecules of a diferent substance B, keeping the volume constant, what is the new equation for the degeneracy?

Answer 1

if we consider a box i.e. in cubical shape such that a=b=c,energy can be expressed by

       E   = h² / 8ma²    (   n_x² + n_y² + n_z² )

   for the lowest quantum state ( 111), in which n_{x ,}n_{y ,}n_z respectively are equal to unity.it is seen that

    E =    3 h²    /   8ma²    there is only set of quantum numbers that gives this energy state& this level is

said to be non degenarate.

if we now consider the second energy state there are three sets (112) (121)   (211 ) of the quantum numbers

n_{x ,}n_y,n_z that will give the same energy level, E = 3h² /4ma²   such level is said to be degenarate&this

particular level is said to degenarate&in this particular level is called Triply degenerate. which is based on

degeneracy of the energy levels in a three dimensional box.

                            thank u