Question

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

Answer 1

`u/n = (-e^2)/(4\pi \epsilon r) (ln2)`

Step-by-step 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 = (-2e^2)/(4\pi \epsilon r) * (1)/(r) * \sum _n {(1)/(n)}(-1)^(n-1)`

we will use here Taylor series approx method

`u = (-e^2)/(2\pi \epsilon r) (ln2)`

and N/2 pair will contribute here

so

`u = (N)/(2) (-e^2)/(2\pi \epsilon r) (ln2)`

so energy per ion will be here

`u/n = (-e^2)/(4\pi \epsilon r) (ln2)`