Question

calculate the potential energy per ion for an infinite one dimensional crystal which will alternate sodium and chloride ions

Answer 1

Answer:

$u/n = \frac{-e^2}{4\pi \epsilon r} (ln2)$

Explanation:

given data

we will take here

sodium ions = positive charge

chloride ions = negative cgarge

solution

as when we take Na positive charge so Number of origin is

d = 0

and here pair of ions with negative charge at d = - r

and d = +r

therefore

$u = \frac{-2e^2}{4\pi \epsilon r} \times \frac{1}{r} \times \sum _n {\frac{1}{n}}(-1)^{n-1}$  

we will use here Taylor series approx method

$u = \frac{-e^2}{2\pi \epsilon r} (ln2)$  

and N/2 pair will contribute here

so

$u = \frac{N}{2} \frac{-e^2}{2\pi \epsilon r} (ln2)$

so energy per ion will be here

$u/n = \frac{-e^2}{4\pi \epsilon r} (ln2)$