To find the energy needed for the conversion, we first need to calculate the number of moles of sodium vapor.

Step 1: Calculate the number of moles of sodium (Na).

Given mass of sodium = 5.75 mg = $5.75\times 10^{-3}$ g

Atomic weight of sodium = 23 g/mol

Number of moles (n) = $\frac{\text{mass}}{\text{molar mass}}=\frac{5.75\times 10^{-3}\text{ g}}{23\text{ g/mol}}$

$n=0.25\times 10^{-3}\text{ mol}=2.5\times 10^{-4}\text{ mol}$

Step 2: Calculate the total energy needed.

Ionization energy of sodium = 490 kJ/mol

Energy needed = Number of moles $\times$ Ionization energy per mole

Energy needed = $2.5\times 10^{-4}\text{ mol}\times 490\text{ kJ/mol}$

Energy needed = $1225\times 10^{-4}\text{ kJ}$

Energy needed = $0.1225\text{ kJ}$

Option Analysis:

• A) 1.96 kJ: This value is incorrect. It might result from calculation errors or incorrect unit conversions.
• B) 1960 kJ: This value is significantly too high, indicating a large error in calculation or unit conversion.
• C) 122.5 kJ: This value is incorrect. It might result from not converting mg to g or other calculation mistakes.
• D) 0.1225 kJ: This is the correct calculated value.

Correct Answer: (D)