The ionisation energy of `10` times innised sodium atom is

Options

A. `13.6 eV`
B. `13.6 ** 11 eV`
C. `13.6/(11^(2)) eV`
D. `13.6 ** (11)^(2) eV`

Answer

To find the ionization energy of a sodium atom that has been ionized 10 times, we can use the formula derived from Bohr's theory for hydrogen-like atoms. Here’s a step-by-step solution:

### Step 1: Understand the Ionization Energy Formula
For hydrogen-like atoms, the energy of an electron in the nth orbit is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \text{ eV} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number.

### Step 2: Identify the Values for Sodium
For sodium (Na), the atomic number \( Z \) is 11. Since we are considering the ionization energy of a sodium atom that has been ionized 10 times, we will look at the state of the electron after it has lost 10 electrons. This means we are effectively considering a sodium ion with a charge of +10, which behaves like a hydrogen-like atom with \( Z = 11 \).

### Step 3: Determine the Principal Quantum Number
For the ground state, the principal quantum number \( n \) is 1.

### Step 4: Calculate the Energy
Substituting the values into the energy formula:
\[ E = -\frac{13.6 \times 11^2}{1^2} \]
Calculating \( 11^2 \):
\[ 11^2 = 121 \]
Now substituting back:
\[ E = -\frac{13.6 \times 121}{1} = -1643.6 \text{ eV} \]

### Step 5: Determine the Ionization Energy
The ionization energy is the negative of the energy calculated:
\[ \text{Ionization Energy} = -E = 1643.6 \text{ eV} \]

### Final Answer
The ionization energy of a sodium atom that has been ionized 10 times is:
\[ \text{Ionization Energy} = 1643.6 \text{ eV} \]

---