Question

The total potential energy describing the NaCl lattice is given by: Utot = [ ( -(αe^2) / (4πε 0r) ) + ( A / r^8 ) ], where a is the Madelung constant (a=1.75 for NaCl) and A is a positive constant.

1. What is the physical meaning of the two terms of Utot? Let r0 be the value of the ionic separation r for which Utot is minimum.

2. Deduce an expression of A as a function of r0. Using r0=0.281nm, extract a value of Utot for r=r0.

The quantity –Utot is the energy required to remove a Na+ ion and a Cl- ion from the lattice. To form a pair of neutral atoms from this pair of ions involves a release of 5.14eV (the ionization energy of Na) and the expenditure of 3.61eV (the electron affinity of Cl).

3. What is the energy required to remove a pair of neutral Na and Cl atoms from the crystal? The experimental value for this quantity is 6.39eV. How well does your calculation agree?

Answer 1

2 O given ( ) ( 0 L + 00 = - 1 2 4T to no I it represent attractive potential it represent the repusive potential present Tenengy. enengy meduing const x=1.75 polental energy = A/S -repusne LO) > * atractive potential energy 4TG no (2) we know at equilibrium [F=0 = По

2 do? 4TT to По +II со 32Тео put value of A in ear (1 - Usotay = - Qe2 + 4-то по" de este 32 тео та put ит = axo1 ) - xo2 4TT (ъ По = - do 2 given, ": d=1:15 medving constat 41 to - 1 ас 32 Т% По - та? 8 (Чto) По По= 0-18 | = - 1x |-75 х (1 6xio ) xqxo1 Вхо 281 x 10 ч

- 389 - - (7x1.75% 16X16 JX9 X 10 X 10' 8x 0.281 8109 - 20 Uttel = - 125.55 x10° dvided by 1:6 x 09. Uporal = -7.84 R ev as given (3) s Natsilyev - wat të I altē ci + 3. blev Na + ci ? Natut (5.14 3.61)ev - ² Natu + 1.51 ev - Nattci. we have total = -7.84 ev! so. energy required to remove a pain of neural na and ci atmo atom from crystal = (-7.84 + 1.51) ev = - 6.33 ev ay Lave sign bound energy, so it agree with expt result nearly ~ 6.39
dear I solved each part clearly......if u have any doubt PlZ comment.

Plz like my answer.......Thank you.