With the help of Bohr 's model , calculate the second ionisation energy of helium (energy required to remove the electron from `He^(o+)`

Explanation

To calculate the second ionization energy of helium (He), which is the energy required to remove the second electron from the ion He⁺ (helium with a +1 charge), we can use Bohr's model of the atom. Here’s a step-by-step solution:

### Step 1: Understand the Ionization Process
The second ionization energy refers to the energy required to remove an electron from He⁺. Helium has an atomic number (Z) of 2, meaning it has 2 protons and, in its neutral state, 2 electrons. The first ionization removes one electron, resulting in He⁺.

### Step 2: Use Bohr's Formula for Energy Levels
According to Bohr's model, the energy of an electron in the nth orbit of a hydrogen-like atom can be calculated using the formula:
\[ E_n = -\frac{1312 \, Z^2}{n^2} \text{ kJ/mol} \]
where:
- \(E_n\) is the energy of the electron in the nth orbit,
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number.

### Step 3: Determine the Values for Helium Ion (He⁺)
For He⁺:
- \(Z = 2\) (since helium has 2 protons),
- \(n = 1\) (the electron is in the first energy level).

### Step 4: Calculate the Energy of the Electron in He⁺
Substituting the values into the formula:
\[ E_1 = -\frac{1312 \times 2^2}{1^2} \]
Calculating this gives:
\[ E_1 = -\frac{1312 \times 4}{1} = -5248 \text{ kJ/mol} \]

### Step 5: Calculate the Second Ionization Energy
The second ionization energy (IE2) is calculated using the formula:
\[ IE_2 = E_{\infty} - E_1 \]
where \(E_{\infty}\) is the energy of an electron when it is completely removed (which is 0 kJ/mol).

Substituting the values:
\[ IE_2 = 0 - (-5248) = 5248 \text{ kJ/mol} \]

### Conclusion
The second ionization energy of helium (He) is:
\[ \text{IE}_2 = 5248 \text{ kJ/mol} \]

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