An electron is to be removed from the first energy level of hydrogen atom .How much energy is required for this purpose ?

Explanation

To determine the energy required to remove an electron from the first energy level of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**:
- When we talk about removing an electron from an atom, we are referring to the process of ionization. In this case, we are removing an electron from the first energy level (n=1) of a hydrogen atom.

2. **Identify the Relevant Formula**:
- The energy of an electron in a hydrogen atom can be calculated using the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \]
- Where:
- \(E\) is the energy of the electron,
- \(Z\) is the atomic number of the element (for hydrogen, \(Z = 1\)),
- \(n\) is the principal quantum number (energy level).

3. **Set Up the Calculation for Ionization**:
- To find the energy required to remove the electron from the first energy level (n=1) to infinity (n=∞), we will use the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \Bigg|_{n=1} \text{ to } n=\infty \]
- This means we will calculate the energy at \(n=1\) and \(n=\infty\).

4. **Calculate the Energy at n=1**:
- Plugging in the values:
\[ E_{n=1} = -\frac{13.6 \times 1^2}{1^2} = -13.6 \, \text{eV} \]

5. **Calculate the Energy at n=∞**:
- At \(n=\infty\), the energy is:
\[ E_{n=\infty} = -\frac{13.6 \times 1^2}{\infty^2} = 0 \, \text{eV} \]

6. **Determine the Energy Required for Ionization**:
- The energy required to remove the electron from n=1 to n=∞ is the difference between the two energy states:
\[ \text{Energy required} = E_{n=\infty} - E_{n=1} = 0 - (-13.6) = 13.6 \, \text{eV} \]

### Final Answer:
The energy required to remove an electron from the first energy level of a hydrogen atom is **13.6 eV**.

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