The ratios for the energy of the electron in a particular orbit of a single electron species are
[Kinetic : Potential ] and [Total : Kinetic ]

Options

A. [1:-2] and [-1:1]
B. [1:2] and [1:1]
C. [1:1] and [1:2]
D. [1:2] and [1:2]

Answer

To solve the problem, we need to determine the ratios of kinetic energy to potential energy and total energy to kinetic energy for an electron in a particular orbit according to Bohr's model.

### Step-by-Step Solution:

1. **Identify the formulas for kinetic and potential energy:**
- According to Bohr's model, the kinetic energy (KE) of an electron in orbit is given by:
\[ KE = \frac{KZe^2}{2R} \]
- The potential energy (PE) of the electron is given by:
\[ PE = -\frac{KZe^2}{R} \]

2. **Calculate the ratio of kinetic energy to potential energy (KE:PE):**
- The ratio can be expressed as:
\[ \frac{KE}{PE} = \frac{\frac{KZe^2}{2R}}{-\frac{KZe^2}{R}} \]
- Simplifying this expression:
\[ \frac{KE}{PE} = \frac{KZe^2}{2R} \cdot \left(-\frac{R}{KZe^2}\right) = \frac{1}{2} \cdot (-1) = -\frac{1}{2} \]
- Therefore, the ratio of kinetic energy to potential energy is:
\[ KE : PE = 1 : -2 \]

3. **Calculate the total energy (TE):**
- The total energy (TE) is given by:
\[ TE = KE + PE = \frac{KZe^2}{2R} - \frac{KZe^2}{R} \]
- Simplifying this:
\[ TE = \frac{KZe^2}{2R} - \frac{2KZe^2}{2R} = -\frac{KZe^2}{2R} \]

4. **Calculate the ratio of total energy to kinetic energy (TE:KE):**
- The ratio can be expressed as:
\[ \frac{TE}{KE} = \frac{-\frac{KZe^2}{2R}}{\frac{KZe^2}{2R}} \]
- Simplifying this expression:
\[ \frac{TE}{KE} = -1 \]
- Therefore, the ratio of total energy to kinetic energy is:
\[ TE : KE = -1 : 1 \]

### Final Ratios:
- The ratio of kinetic energy to potential energy is **1 : -2**.
- The ratio of total energy to kinetic energy is **-1 : 1**.