Question

Q2. It is given that the net potential energy ?_? of a system of two atoms varies as a function of their separation distance r as follow:

?_? = − A/ ? ^? + ?/ ?^?

where − ?/ ? ^? is the energy of attraction, and ?/ ?^? is the energy of repulsion.

(a) Show that at equilibrium the energy of attraction is ?/? times the energy of repulsion, and derive an expression to calculate the bond energy ?_? and the equilibrium interatomic spacing ?_?.

(b) State your registration number in the form YZ PWMEC HIJK.(use registration no as 18PWMEC4545)

For a hypothetical X⁺ - Y ^- ion pair, the attractive and repulsive energies E_A and E_R, respectively, depend on the distance between the ions r according to the following equations:

?_? = − ? . ???/ ?

?? = ?. ?? × ??−?/ ? ^?

For these expressions, energies are expressed in electron volts (per X⁺ - Y ^- pair), and r is the distance in nanometers. The net energy E_N is just the sum of the preceding two expressions. Superimpose on a single plot E_N, E_R, and E_A versus r up to 1.0 nm. On the basis of this plot, determine the equilibrium spacing ?0 between the X+ and Yions, and the magnitude of the bonding energy E0 between the two ions. Mathematically determine the ?_? and ?_? values using your answers to part (a), and compare them to the graphical results obtained above.

Answer 1