Energy required for the ionisation of 0.02 gram atom of magnesium is x k J . The amount of energy required to ionise 1 atom of magneslum is

Options

A. xkJ
B. `(X)/(0.02N_(A))` J
C. `("xx"10^(3))/(0.02N_(A))` J
D. `xN_(A)kJ`

Answer

To find the amount of energy required to ionize one atom of magnesium given that the energy required to ionize 0.02 gram atoms of magnesium is \( x \) kJ, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Gram Atom and Moles**:
- A gram atom (or gram-mole) of an element is equivalent to one mole of that element. Thus, 0.02 gram atoms of magnesium is equal to 0.02 moles of magnesium.

2. **Using Avogadro's Number**:
- One mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.), which is approximately \( 6.022 \times 10^{23} \). Therefore, 0.02 moles of magnesium contains:
\[ 0.02 \times 6.022 \times 10^{23} \text{ atoms} \]

3. **Energy Required for Ionization**:
- The energy required to ionize 0.02 moles of magnesium is given as \( x \) kJ. This means that the energy required to ionize \( 0.02 \times 6.022 \times 10^{23} \) atoms is \( x \) kJ.

4. **Calculating Energy per Atom**:
- To find the energy required to ionize one atom of magnesium, we divide the total energy by the number of atoms in 0.02 moles:
\[ \text{Energy per atom} = \frac{x \text{ kJ}}{0.02 \times 6.022 \times 10^{23}} \]

5. **Converting kJ to Joules**:
- Since \( 1 \text{ kJ} = 1000 \text{ J} \), we can convert the energy from kilojoules to joules:
\[ \text{Energy per atom in Joules} = \frac{x \times 1000 \text{ J}}{0.02 \times 6.022 \times 10^{23}} \]

6. **Final Expression**:
- Therefore, the energy required to ionize one atom of magnesium is:
\[ \text{Energy per atom} = \frac{x \times 1000}{0.02 \times 6.022 \times 10^{23}} \text{ J} \]