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. `("x*"10^(3))/(0.02N_(A))` J
D. `xN_(A)kJ`

Answer

To solve the problem of determining the 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 1: Understand the Given Information
We know that the energy required to ionize 0.02 gram atoms of magnesium is \( x \) kJ. We need to find out how much energy is required to ionize just one atom of magnesium.

### Step 2: Calculate the Number of Moles of Magnesium
The molar mass of magnesium (Mg) is approximately 24 g/mol. To find the number of moles in 0.02 gram atoms of magnesium, we use the formula:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{0.02 \, \text{g}}{24 \, \text{g/mol}} = \frac{0.02}{24} = \frac{1}{1200} \, \text{mol} \]

### Step 3: Calculate the Number of Atoms in 0.02 gram atoms of Magnesium
Using Avogadro's number (\( N_a \approx 6.022 \times 10^{23} \) atoms/mol), we can find the number of atoms in \( \frac{1}{1200} \) moles of magnesium:

\[ \text{Number of atoms} = \left(\frac{1}{1200} \, \text{mol}\right) \times N_a = \frac{N_a}{1200} \]

### Step 4: Relate Energy to the Number of Atoms
According to the problem, the energy required to ionize \( \frac{N_a}{1200} \) atoms of magnesium is \( x \) kJ. Therefore, the energy required to ionize one atom of magnesium can be calculated as follows:

\[ \text{Energy per atom} = \frac{x \, \text{kJ}}{\frac{N_a}{1200}} = \frac{x \times 1200}{N_a} \, \text{kJ} \]

### Step 5: Convert kJ to Joules
Since \( 1 \, \text{kJ} = 1000 \, \text{J} \), we convert the energy from kJ to J:

\[ \text{Energy per atom in Joules} = \frac{x \times 1200 \times 1000}{N_a} \, \text{J} = \frac{x \times 10^3}{0.02 \times N_a} \, \text{J} \]

### Final Answer
Thus, the amount of energy required to ionize one atom of magnesium is:

\[ \frac{x \times 10^3}{0.02 N_a} \, \text{J} \]