Estimate the radius of the cesium ion, Cs+. The lattice energy of cesium chloride, CsCl, is 633 kJ/mol. For CsCl, the Madelung constant M is 1.763, and the Born exponent n is 10.7. The radius of Cl− is known to be 1.81 A˚. Express your answer in Angstroms.
Can you show all working, I'm not sure where to begin? Thanks.

Question

Estimate the radius of the cesium ion, Cs+. The lattice energy of cesium chloride, CsCl, is 633 kJ/mol. For CsCl, the Madelung constant M is 1.763, and the Born exponent n is 10.7. The radius of Cl− is known to be 1.81 A˚. Express your answer in Angstroms.
Can you show all working, I'm not sure where to begin? Thanks.

anonymous · Answer

The equation is the same as determining the force of attraction between two charges, just changed a bit.|dw:1352059433235:dw|

Ke is the coloumb constant, q1 and q2 are the elementary charges of the ions, r is the radius distance from ionic nucleus to nucleus(in this case, it would be the radius of the chlorine, added to the unknown X radius of Cs). M is the Madelung constant, and the 1/n term refers to the Born repulsion exponent.

You just need to perform the algebra to isolate the Cs radius, and solve the equation.

Keep in mind, this equation determines the J/ion energy, so you must convert your kJ/mol term into just J/ion.