Total energy of an electron in the hydrogen atom in the ground state is -13.6 eV. The potential energy of this electron is

Options

A. 13.6 eV
B. 0
C. `-27.2` eV
D. `-13.6` eV

Answer

To find the potential energy of an electron in a hydrogen atom in the ground state, we can follow these steps:

### Step 1: Understand the relationship between total energy and potential energy
In Bohr's model of the hydrogen atom, the total energy (E) of an electron in an orbit is related to its potential energy (U) by the equation:
\[ U = 2E \]
This means that the potential energy is twice the total energy.

### Step 2: Identify the total energy
From the problem, we know that the total energy of the electron in the ground state is:
\[ E = -13.6 \, \text{eV} \]

### Step 3: Calculate the potential energy
Using the relationship \( U = 2E \):
\[ U = 2 \times (-13.6 \, \text{eV}) \]
\[ U = -27.2 \, \text{eV} \]

### Step 4: Conclusion
The potential energy of the electron in the hydrogen atom in the ground state is:
\[ U = -27.2 \, \text{eV} \]

Thus, the answer is \(-27.2 \, \text{eV}\).

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