Question

Consider the states of the combined total spin of two particles, each of which has spin 5/2 with m_s= +5/2, +3/2, +1/2, −1/2, −3/2, and −5/2.

(a) How many macrostates are there corresponding to the different values of the total spin if the particles are distinguishable?

(b) If the two particles are distinguishable, what is the total number of microstates for all the allowed macrostates?

(c) If the two particles are indistinguishable, what is the total number of microstates for all the allowed macrostates?

(d) What are the allowed values for the total spin if the two particles are indistinguishable?

Answer 1

The table shown below will clarify the no.of macro and micro-states.

(a)

The different macro-states are (possible total spins, doesn't matter if particles are distinguishable or not.)

hence 11.

(b)

No.of micro-states are respectively,

which make a total of 36 micro-states if the particles are distinguishable.

(c)

If the particles are indistinguishable, then no.of micro-states are respectively,

which make a total of 21 micro-states if the particles are distinguishable.

(d) Already answered in (a).