If ionising energy of H atom is 13.6 eV, then the second ionising energy of He should be

Options

A. `13.6 eV`
B. `27.2 eV`
C. `54.4 eV`
D. Cannot be predicted

Answer

To find the second ionization energy of helium (He) given that the ionization energy of hydrogen (H) is 13.6 eV, we can follow these steps:

### Step 1: Understand the Ionization Energy of Hydrogen
The ionization energy of hydrogen (H) is given as 13.6 eV. This value represents the energy required to remove the only electron from a hydrogen atom.

### Step 2: Identify the Structure of Helium
Helium has two electrons. The first ionization energy (IE1) is the energy required to remove one electron from helium, and the second ionization energy (IE2) is the energy required to remove the second electron after the first one has been removed.

### Step 3: Calculate the Energy of the Second Electron in Helium
To find the second ionization energy of helium, we can use the formula for the energy of an electron in a hydrogen-like atom:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where:
- \( Z \) is the atomic number (for helium, \( Z = 2 \))
- \( n \) is the principal quantum number (for the second electron in helium, \( n = 2 \))

### Step 4: Substitute Values into the Formula
Using the values for helium:
\[ E_2 = -\frac{13.6 \, \text{eV} \cdot 2^2}{2^2} \]
\[ E_2 = -\frac{13.6 \, \text{eV} \cdot 4}{4} \]
\[ E_2 = -54.4 \, \text{eV} \]

### Step 5: Determine the Second Ionization Energy
The second ionization energy (IE2) is the energy required to remove the second electron, which is equal to the absolute value of the energy calculated:
\[ \text{IE2} = 54.4 \, \text{eV} \]

### Conclusion
Thus, the second ionization energy of helium is 54.4 eV.

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