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. Zero
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 use the relationship between total energy, kinetic energy, and potential energy. Here’s a step-by-step solution:

### Step 1: Understand the relationship between total energy, kinetic energy, and potential energy.
The total energy (E) of an electron in a hydrogen atom is given by the equation:
\[ E = K + U \]
where \( K \) is the kinetic energy and \( U \) is the potential energy.

### Step 2: Use the known values.
From the question, we know that the total energy in the ground state of the hydrogen atom is:
\[ E = -13.6 \, \text{eV} \]

### Step 3: Relate potential energy and kinetic energy.
In a hydrogen atom, the potential energy is related to the kinetic energy by the equation:
\[ U = -2K \]

### Step 4: Express kinetic energy in terms of total energy.
Since we have \( E = K + U \) and \( U = -2K \), we can substitute \( U \) into the total energy equation:
\[ E = K - 2K = -K \]
This implies:
\[ K = -E \]

### Step 5: Substitute the value of total energy to find kinetic energy.
Substituting the value of total energy:
\[ K = -(-13.6 \, \text{eV}) = 13.6 \, \text{eV} \]

### Step 6: Calculate potential energy using kinetic energy.
Now, we can find the potential energy using the relationship \( U = -2K \):
\[ U = -2 \times 13.6 \, \text{eV} = -27.2 \, \text{eV} \]

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