The ground state energy of hydrogen atom is -13.6eV. What is the K.E. of electron in this state?

Options

A. `2.18xx10^(-14)J`
B. `2.18xx10^(-16)J`
C. `2.18xx10^(-18)J`
D. `2.18xx10^(-19)J`

Explanation

To find the kinetic energy (K.E.) of the electron in the ground state of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between total energy (E), kinetic energy (K.E.), and potential energy (P.E.)**:
- The total energy of an electron in a hydrogen atom is given by:
\[ E = K.E. + P.E. \]
- For a hydrogen atom, the kinetic energy is related to the total energy by:
\[ K.E. = -E \]
- The potential energy is related to the total energy by:
\[ P.E. = 2E \]

2. **Identify the total energy of the hydrogen atom**:
- The ground state energy of the hydrogen atom is given as:
\[ E = -13.6 \, \text{eV} \]

3. **Calculate the kinetic energy using the relationship**:
- Substitute the total energy into the kinetic energy formula:
\[ K.E. = -(-13.6 \, \text{eV}) = 13.6 \, \text{eV} \]

4. **Convert the kinetic energy from electron volts to joules**:
- We know that:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
- Therefore, to convert 13.6 eV to joules:
\[ K.E. = 13.6 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]
- Calculate the value:
\[ K.E. = 21.76 \times 10^{-19} \, \text{J} = 2.176 \times 10^{-18} \, \text{J} \]

5. **Final Result**:
- The kinetic energy of the electron in the ground state of the hydrogen atom is:
\[ K.E. = 2.18 \times 10^{-18} \, \text{J} \]

### Summary:
The kinetic energy of the electron in the ground state of a hydrogen atom is \( 2.18 \times 10^{-18} \, \text{J} \).