The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is

Options

A. `2:-1`
B. `1:-1`
C. `1:1`
D. `1:-2`

Explanation

To solve the problem of finding the ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Energies in a Bohr Atom:**
- In a Bohr model of the hydrogen atom, the total energy (E) of the electron in a specific orbit is given by the formula:
\[ E = -\frac{K e^2}{2r} \]
where \( K \) is Coulomb's constant, \( e \) is the charge of the electron, and \( r \) is the radius of the orbit.

2. **Kinetic Energy of the Electron:**
- The kinetic energy (K.E) of the electron in the orbit can be expressed as:
\[ K.E = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the electron and \( v \) is its velocity.

3. **Relating Kinetic Energy to Total Energy:**
- According to the Bohr model, the total energy is related to the kinetic energy by the equation:
\[ K.E = -\frac{1}{2}E \]
- This means that the kinetic energy is equal to half the magnitude of the total energy but with a negative sign.

4. **Finding the Ratio:**
- To find the ratio of kinetic energy to total energy, we can write:
\[ \text{Ratio} = \frac{K.E}{E} \]
- Substituting the relationship we found:
\[ \text{Ratio} = \frac{-\frac{1}{2}E}{E} = -\frac{1}{2} \]

5. **Conclusion:**
- Therefore, the ratio of kinetic energy to total energy of an electron in a Bohr orbit of the hydrogen atom is:
\[ \frac{K.E}{E} = -\frac{1}{2} \]

### Final Answer:
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is \(-\frac{1}{2}\).