Question

4. A certain molecule can exist in either a non-degenerate singlet state or a triplet state (with degeneracy 3). The energy of the triplet exceeds that of the singlet by E. Assuming that the molecules are distinguishable (localized) and independent, (a) obtain the expression for the molecular partition function. (b) Find expressions in terms of e for the molar energy, molar heat capacity, and molar entropy of such molecules and calculate their values at T = E/k.

Answer 1

solution: 1 * from the data Page 1 - The energy of the triplet excess that of the singlet by E. => Assume the molecules are distinguishable (localized) and independent. a) To obtain the molecular partition function - → 9- Çgi £i/Ket q=g, E, + 9 Ez = q = 1.8, +3 E2 Here, Ez — = (triplet) (singlet) given &, -E,=E

Page 2 b) for molar energy q=1..C./KGT + 3€ €1/KT DECE1/VT + 36-Ez/K meleculars Partition function: - for molar energy: U-UG) == 0 ) (whese, B-#) - BE PE (8294-34,2=PL) E a Mora Pio (fie fel + 342.492) N at T= {/k; then B= 1 * = // put . N . lee Eile +3&e 22/6) U-00) = ---.. -tale (8,6 (+38€ if &, -0 (ground state) then {={+E = E +0=E ; for N=1

Page-3 3 =) U-U(o)= IN 3E + 2 peti; u-ves a et (0+362") => -ule) = (34 ") => 0-ure) .: Ju-vos-en Molar heat capacity. . Cvs U-VC) => Cv - Get N at T- => cve Ž >> Cveta for 1 - 3K et3 (w = 3P ( R = 2 e Regen constant)

Page-4 molar entropy:- 1.5= 0. Hot Nk Ang =>5 - 94 +Nx.dn (64 km ze 3/8) 35=(26)* +Nx ln (1 +32°C/KT) s- en wa* + nk In (1432*+/kr) at T= E/K (: Here, R = nk) >> S- EN K + NK In (1+30-1) (s. 3R + R ln (ex3] S If you satisfied this answer, please give me positive like.