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Working from Krane's Modern Physics 11.5
Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice.
I believe the formula I'm supposed to use is
[tex] U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R}[/tex]
Just from looking in the chapter I can see this is a bcc type lattice with an [itex]\alpha[/itex] of 1.7627, but I'm not sure how they're getting the answer in the back of the book which is;
[tex] U_{c}\,=\,-\frac{e^{2}}{4\pi\epsilon_{0}R}\left(8-\frac{6}{2/\sqrt{3}} + \frac{24}{\sqrt{11/3}}\right)[/tex]
There's an example in the book showing the same procedure for an fcc lattice (NaCl) and that converging term is,
[tex] 6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\ldots[/tex]
but it doesn't derive it, so I'm not really sure how they get it.
Just looking for a few pointers, thanks.
Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice.
I believe the formula I'm supposed to use is
[tex] U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R}[/tex]
Just from looking in the chapter I can see this is a bcc type lattice with an [itex]\alpha[/itex] of 1.7627, but I'm not sure how they're getting the answer in the back of the book which is;
[tex] U_{c}\,=\,-\frac{e^{2}}{4\pi\epsilon_{0}R}\left(8-\frac{6}{2/\sqrt{3}} + \frac{24}{\sqrt{11/3}}\right)[/tex]
There's an example in the book showing the same procedure for an fcc lattice (NaCl) and that converging term is,
[tex] 6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\ldots[/tex]
but it doesn't derive it, so I'm not really sure how they get it.
Just looking for a few pointers, thanks.