The ionization energies of Li and Na are `520 kJ mol ^-1 and 495 kJ mol ^-1` respectively. The energy required to convert all the atoms present in 7 mg of Li vapours and 23 mg of sodium vapours to their respective gaseous captions respectively are :

Options

A. 52 J,49.5 J
B. 520 J,495 J
C. 49.5 J,52 J
D. 495 J,520 J

Explanation

To solve the problem of determining the energy required to convert 7 mg of lithium vapors and 23 mg of sodium vapors to their respective gaseous cations, we can follow these steps:

### Step 1: Understand Ionization Energy
Ionization energy is the energy required to remove an electron from an isolated gaseous atom in its ground state. For lithium (Li) and sodium (Na), the ionization energies are given as:
- Li: 520 kJ/mol
- Na: 495 kJ/mol

### Step 2: Convert Mass to Moles
To find out how much energy is required for the given masses of lithium and sodium, we first need to convert the masses from milligrams to moles.

1. **For Lithium (Li)**:
- Molar mass of Li = 6.94 g/mol
- Convert 7 mg to grams:
\[ 7 \text{ mg} = 0.007 \text{ g} \]
- Calculate moles of Li:
\[ \text{Moles of Li} = \frac{0.007 \text{ g}}{6.94 \text{ g/mol}} \approx 0.00101 \text{ mol} \]

2. **For Sodium (Na)**:
- Molar mass of Na = 22.99 g/mol
- Convert 23 mg to grams:
\[ 23 \text{ mg} = 0.023 \text{ g} \]
- Calculate moles of Na:
\[ \text{Moles of Na} = \frac{0.023 \text{ g}}{22.99 \text{ g/mol}} \approx 0.00100 \text{ mol} \]

### Step 3: Calculate Energy Required
Now, we can calculate the energy required to ionize the respective amounts of lithium and sodium.

1. **For Lithium**:
- Energy required = Ionization energy × Moles of Li
\[ \text{Energy for Li} = 520 \text{ kJ/mol} \times 0.00101 \text{ mol} \approx 0.525 \text{ kJ} \approx 525 \text{ J} \]

2. **For Sodium**:
- Energy required = Ionization energy × Moles of Na
\[ \text{Energy for Na} = 495 \text{ kJ/mol} \times 0.00100 \text{ mol} \approx 0.495 \text{ kJ} \approx 495 \text{ J} \]

### Step 4: Final Results
- Energy required to ionize 7 mg of Li: **525 J**
- Energy required to ionize 23 mg of Na: **495 J**

### Summary
The energy required to convert all the atoms present in 7 mg of lithium vapors and 23 mg of sodium vapors to their respective gaseous cations are:
- **Lithium**: 525 J
- **Sodium**: 495 J