The ratio of potential energy and total energy of an electron in a Bohr of a hydrogen -like species is

Options

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

Explanation

To find the ratio of potential energy to total energy of an electron in a Bohr model of a hydrogen-like species, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Potential Energy (PE)**:
The potential energy (PE) of an electron in a Bohr model for a hydrogen-like atom is given by the formula:
\[ PE = -\frac{Z e^2}{R} \]
where \( Z \) is the atomic number, \( e \) is the charge of the electron, and \( R \) is the radius of the orbit.

2. **Identify the Total Energy (TE)**:
The total energy (TE) of an electron in a Bohr model is given by:
\[ TE = -\frac{Z e^2}{2R} \]

3. **Set Up the Ratio**:
We need to find the ratio of potential energy to total energy:
\[ \text{Ratio} = \frac{PE}{TE} \]

4. **Substitute the Formulas**:
Substitute the expressions for PE and TE into the ratio:
\[ \text{Ratio} = \frac{-\frac{Z e^2}{R}}{-\frac{Z e^2}{2R}} \]

5. **Simplify the Ratio**:
The negative signs cancel out, and we can simplify the ratio:
\[ \text{Ratio} = \frac{\frac{Z e^2}{R}}{\frac{Z e^2}{2R}} = \frac{Z e^2}{R} \times \frac{2R}{Z e^2} \]
Here, \( Z e^2 \) and \( R \) cancel out:
\[ \text{Ratio} = 2 \]

6. **Conclusion**:
Therefore, the ratio of potential energy to total energy of an electron in a Bohr model of a hydrogen-like species is:
\[ \text{Ratio} = 2 \]

### Final Answer:
The ratio of potential energy to total energy of an electron in a Bohr model of a hydrogen-like species is **2**.