Complete the table for coordination number and number of particles per unit cell.

c)

Step 1: Complete the table for coordination number and number of particles per unit cell.

Type of unit cell	Coordination number	Number of particles per unit cell
Cubic close pack or face centered cubic	12	4
Body centered cubic	8	2

d)

i) Lattice energy is the energy change when one mole of an ionic compound is formed from its gaseous ions under standard conditions. It is a measure of the strength of the electrostatic forces between ions in a crystal lattice.

ii) Born-Haber cycle for the formation of sodium oxide ($\text{Na}_2\text{O}$).
The overall reaction is: $2\text{Na(s)} + \frac{1}{2}\text{O}_2(\text{g}) \rightarrow \text{Na}_2\text{O(s)}$

$$\begin{array}{c} 2\text{Na(s)} + \frac{1}{2}\text{O}_2(\text{g}) \xrightarrow{\Delta H_f} \text{Na}_2\text{O(s)} \\ \downarrow 2\Delta H_{atom}(\text{Na}) \\ 2\text{Na(g)} + \frac{1}{2}\text{O}_2(\text{g}) \\ \downarrow \Delta H_{atom}(\text{O}) \\ 2\text{Na(g)} + \text{O(g)} \\ \downarrow 2IE_1(\text{Na}) \\ 2\text{Na}^+(\text{g}) + \text{O(g)} + 2\text{e}^- \\ \downarrow EA_1(\text{O}) \\ 2\text{Na}^+(\text{g}) + \text{O}^-(\text{g}) + \text{e}^- \\ \downarrow EA_2(\text{O}) \\ 2\text{Na}^+(\text{g}) + \text{O}^{2-}(\text{g}) \\ \downarrow U_L \\ \text{Na}_2\text{O(s)} \end{array}$$

iii) From the Born-Haber cycle, the expression for the lattice energy ($U_L$) of sodium oxide is:

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