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

Options

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

Explanation

To find the ratio of kinetic energy (K.E.) to the total energy (T.E.) of an electron in a Bohr orbit of the hydrogen atom, we can follow these steps:

### Step 1: Understand the Definitions
- **Kinetic Energy (K.E.)** of the electron in a Bohr orbit is given by the formula:
\[ K.E. = -\frac{1}{2} E \]
- **Total Energy (T.E.)** of the electron in a Bohr orbit is given by:
\[ T.E. = K.E. + P.E. \]
where P.E. is the potential energy.

### Step 2: Express Total Energy
From the Bohr model, we know:
- The potential energy (P.E.) is given by:
\[ P.E. = -\frac{z e^2}{4 \pi \epsilon_0 r} \]
- The total energy can be expressed as:
\[ T.E. = K.E. + P.E. \]

### Step 3: Relate K.E. and T.E.
From the Bohr model, we also know that:
- The kinetic energy is equal to half the magnitude of the potential energy:
\[ K.E. = -\frac{1}{2} P.E. \]
Thus, we can express the total energy in terms of kinetic energy:
\[ T.E. = K.E. + P.E. = K.E. - 2K.E. = -K.E. \]

### Step 4: Calculate the Ratio
Now, we can find the ratio of kinetic energy to total energy:
\[ \frac{K.E.}{T.E.} = \frac{K.E.}{-K.E.} = -1 \]

### Conclusion
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:
\[ \frac{K.E.}{T.E.} = -1 \]