Define ionisation energy. What is the value for a hydrogen atom?

Options

A. `3.4 eV`
B. `10.4 eV`
C. `12.09 eV`
D. `13.6 eV`

Explanation

### Step-by-Step Solution:

1. **Definition of Ionization Energy**:
- Ionization energy is defined as the minimum amount of energy required to remove an electron from an atom or ion in its ground state, allowing the electron to escape from the influence of the nucleus.

2. **Understanding Energy Levels**:
- Atoms have different energy levels, often referred to as orbits. For hydrogen, the energy of an electron in the nth orbit can be calculated using the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
- Here, \(E_n\) is the energy of the electron in the nth orbit, and \(n\) is the principal quantum number (1 for the ground state).

3. **Calculating Ionization Energy for Hydrogen**:
- For a hydrogen atom, the electron in the ground state is in the first orbit (n=1). Thus, we substitute \(n=1\) into the energy formula:
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]
- The negative sign indicates that the electron is bound to the nucleus.

4. **Energy Required for Ionization**:
- To ionize the hydrogen atom, we need to provide enough energy to overcome the binding energy of the electron. This means we need to supply energy equal to the absolute value of the energy at n=1:
\[ \text{Ionization Energy} = 13.6 \, \text{eV} \]

5. **Conclusion**:
- Therefore, the ionization energy for a hydrogen atom is 13.6 eV.