Problem 1 . Consider a hypothetical X+ - Y- ion pair. The atomic radii of the ca

Question

Problem 1 . Consider a hypothetical X+ - Y- ion pair. The atomic radii of the cation and anion are 1.4 A and 1.3 A, respectively. Answer the questions (a)-(c) below.
(a) Calculate the equilibrium interatomic separation between X+ and Y-.
(b) Calculate the force of attraction between these ions in equilibrium.

(c) Calculate the force of repulsion between these ions in equilibrium.
Hints:
(a) In equilibrium, the ions just touch one another.
(b) Use the Coulomb's law, which summarizes the relationship between the attractive energy and interatomic separation [see Eqs. (2.9), (2.10)] and the relationship between the force and energy [see Eqs. (2.5b), (2.8b)]. Read section 2.6 for more information.

(c) The total force in equilibrium is known, and equal to the sum of its attractive and repulsive components. Read section 2.5 for more information.

Explanation / Answer

(a) The equilibrium interatomic separation between X+ and Y-

= 1.4 + 1.3 = 2.7 Angstrom

(b) Force of attraction F(A) between these ions

= A/r^2 = (Z1e)(Z2e)/4pier^2

where,

Z1 and Z2 are charge on each ion = 1

e = 1.6 x 10^-19 C

e = 8.85 x 10^-12 F/m

r = 2.7 x 10^-10 m

Feed values,

F(A) = (1)(1)(1.6 x 10^-19)^2/(4 x 3.1416 x 8.85 x 10^-12 x (2.7 x 10^-10)^2)

        = 3.16 x 10^-9 N

(c) F(repulsion) = Net Force - F(A)

where, Net Force = 0

So, F(repulsion) between these ions = -3.16 x 10^-9 N

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