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 question regarding the ratios of the energy of the electron in a particular orbit of a single electron species, we will follow these steps:

### Step 1: Understand the Energy Expressions
According to the Bohr model, the kinetic energy (KE), potential energy (PE), and total energy (TE) of an electron in orbit can be expressed as:
- Kinetic Energy (KE) = \( \frac{kZ e^2}{2R} \)
- Potential Energy (PE) = \( -\frac{kZ e^2}{R} \)
- Total Energy (TE) = \( -\frac{kZ e^2}{2R} \)

### Step 2: Calculate the Ratio of Kinetic Energy to Potential Energy
To find the ratio of kinetic energy to potential energy (KE : PE), we use the expressions derived above:
\[ \text{KE : PE} = \frac{\frac{kZ e^2}{2R}}{-\frac{kZ e^2}{R}} \]
This simplifies as follows:
\[ = \frac{kZ e^2}{2R} \times \frac{R}{-kZ e^2} = \frac{1}{-2} = -\frac{1}{2} \]
Thus, the ratio can be expressed as:
\[ \text{KE : PE} = 1 : -2 \]

### Step 3: Calculate the Ratio of Total Energy to Kinetic Energy
Next, we calculate the ratio of total energy to kinetic energy (TE : KE):
\[ \text{TE : KE} = \frac{-\frac{kZ e^2}{2R}}{\frac{kZ e^2}{2R}} \]
This simplifies to:
\[ = -1 \]
Thus, we can express this ratio as:
\[ \text{TE : KE} = -1 : 1 \]

### Step 4: Summarize the Ratios
From our calculations, we have the following ratios:
- Kinetic Energy to Potential Energy (KE : PE) = \( 1 : -2 \)
- Total Energy to Kinetic Energy (TE : KE) = \( -1 : 1 \)

### Conclusion
Therefore, the final ratios for the energy of the electron in a particular orbit of a single electron species are:
- Kinetic : Potential = \( 1 : -2 \)
- Total : Kinetic = \( -1 : 1 \)