In the ground state energy of hydrogen atom is -13.6, find the potential energy of electron (in joule) in the given state.

Options

A. `-4.36xx10^(-14)J`
B. `-4.36xx10^(-16)J`
C. `-4.36xx10^(-17)J`
D. `-4.36xx10^(-18)J`

Explanation

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

### Step 1: Understand the relationship between total energy, kinetic energy, and potential energy
In a hydrogen atom, the relationships are given by:
- Kinetic Energy (KE) = - Total Energy (TE)
- Potential Energy (PE) = 2 * Total Energy (TE)

### Step 2: Identify the total energy of the hydrogen atom
From the question, we know that the total energy (TE) of the hydrogen atom in the ground state is:
\[ TE = -13.6 \, \text{eV} \]

### Step 3: Calculate the potential energy using the relationship
Using the relationship for potential energy:
\[ PE = 2 \times TE \]
Substituting the value of total energy:
\[ PE = 2 \times (-13.6 \, \text{eV}) \]
\[ PE = -27.2 \, \text{eV} \]

### Step 4: Convert potential energy from electron volts to joules
We know that:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Now, we can convert the potential energy into joules:
\[ PE = -27.2 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]
\[ PE = -43.52 \times 10^{-19} \, \text{J} \]
\[ PE = -4.352 \times 10^{-18} \, \text{J} \]

### Final Answer
The potential energy of the electron in the ground state of the hydrogen atom is:
\[ PE = -4.352 \times 10^{-18} \, \text{J} \]

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