Energy of electron in the H-atom is determined by

Options

A. only n
B. both n and l
C. n, l and m
D. all the four quantum numbers.

Answer

To determine the energy of an electron in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- In quantum mechanics, electrons in an atom are described by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s).

2. **Identifying the Relevant Quantum Numbers**:
- For the hydrogen atom, which has only one electron, we focus primarily on the principal quantum number (n) and the azimuthal quantum number (l).
- The principal quantum number (n) indicates the energy level of the electron, while the azimuthal quantum number (l) indicates the shape of the orbital.

3. **Calculating Energy**:
- The energy of an electron in a hydrogen atom is primarily determined by the principal quantum number (n).
- The formula for the energy levels of hydrogen is given by:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
- This shows that the energy depends only on n and not on l or any other quantum numbers.

4. **Considering the Case of Hydrogen**:
- In the case of hydrogen (H atom), since it has only one electron, the value of l for the ground state (1s) is 0.
- Therefore, the energy of the electron is determined solely by the value of n.

5. **Conclusion**:
- Since the energy of the electron in a hydrogen atom is determined only by the principal quantum number (n), the correct answer is that the energy is determined by **n**.

### Final Answer:
The energy of the electron in the H atom is determined by **n**.

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