For hydrogen atom, energy of nth level is given by

Options

A. `E_n=-(13.6/n)eV`
B. `E_n=+(13.6/n)eV`
C. `E_n=(13.6/n^2)eV`
D. `E_n=-(13.6/n^2)eV`

Answer

To find the energy of the nth level of a hydrogen atom, we can use Bohr's theory of the hydrogen atom. The energy of an electron in the nth orbit is given by the formula:

1. **Identify the formula for energy levels in hydrogen:**
The energy of the nth level (En) for a hydrogen atom can be expressed as:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where:
- \( E_n \) is the energy of the nth level,
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( n \) is the principal quantum number (the level of the electron).

2. **Substituting the values for hydrogen:**
Since hydrogen has an atomic number \( Z = 1 \), we can substitute this value into the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot 1^2}{n^2} \]

3. **Simplifying the expression:**
This simplifies to:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

4. **Final expression:**
Therefore, the energy of the nth level of a hydrogen atom is given by:
\[ E_n = -\frac{13.6}{n^2} \, \text{eV} \]