1) Consider a system of N distinguishable atoms fixed in a lattice each of which

ID: 1767868 • Letter: 1

Question

1) Consider a system of N distinguishable atoms fixed in a lattice each of which has m

equally spaced energy levels: E1 = 0, E2 = ?, E3 = 2?, . . . , Em = (m ? 1)?.

(a) If the system is in thermodynamic equilibrium, what is the minimum energy per atom

E/N of the system?

(b) If the system is in thermodynamic equilibrium, what is the maximum energy per atom

E/N of the system?

(c) If the system is not required to be in thermodynamic equilibrium, what is the maximum energy per atom E/N of the system?

IF THE SYSTEM HAS N DISTINGUISHABLE ATOMS FIXED IN A LATTICE THEN THE

TOTAL ENERGY OF THE SYSTEM[MINIMUM WHEN ALL THE ATOMS ARE IN THE E1 STATE HAVING ENERGY =0

= [E1+E2+...........EN]=0

AND THE ENERGY PER ATOM OF THE SYSTEM = E TOTAL /N =0

B]THE MAXIMUM ENERGY IS WHEN ALL THE ATOMS ARE IN THE N TH ENERGY STATE

SO THE TOTAL ENERGY = N [(m ? 1)?

SO THE MAXIMUM ENERGY PER ATOM IS

= N [(m ? 1)?/N

=(m ? 1)?

C]IF NOT REQUIRED TO REMAIN IN EQUILLIBRIUM THAN THE SUM OF THE TOTAL ENERGY

IS = [SUM OF THE INDIVIDUAL ATOMS AT EACH ENERGY LEVELS ]

= E1 + E2 ........EN

=[0+ ?+......(m ? 1)?] /N

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