The total energy of electron in the first excited state of hydrogen is about -3.4eV. Find potential energy of electron in this state.

Options

A. `-3.8eV`
B. `-6.8eV`
C. `3.8eV`
D. `6.8eV`.

Answer

To find the potential energy of the electron in the first excited state of hydrogen, we can use the relationship between total energy and potential energy in a hydrogen atom.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The total energy (E) of an electron in a hydrogen atom is related to its potential energy (U) by the equation:
\[ E = \frac{U}{2} \]
This means that the potential energy is twice the total energy.

2. **Identify Total Energy**:
From the problem, we know that the total energy of the electron in the first excited state is:
\[ E = -3.4 \, \text{eV} \]

3. **Calculate Potential Energy**:
Using the relationship from step 1, we can express potential energy as:
\[ U = 2E \]
Substituting the value of E:
\[ U = 2 \times (-3.4 \, \text{eV}) = -6.8 \, \text{eV} \]

4. **Conclusion**:
Therefore, the potential energy of the electron in the first excited state of hydrogen is:
\[ U = -6.8 \, \text{eV} \]

### Final Answer:
The potential energy of the electron in the first excited state of hydrogen is **-6.8 eV**.