A charged particle oscillates about its mean equilibrium position with a frerquency of `10^9 H_z`. The electromagnetic waves produced.

Options

A. will have frequency of `10^9 H_z`
B. will have frequency of `2xx10^9 H_z`
C. will have a wavelength of `0.3 m`
D. fall in the region of radio waves.

Explanation

To solve the problem regarding the electromagnetic waves produced by a charged particle oscillating about its mean equilibrium position, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequency of the Charged Particle**:
The problem states that the charged particle oscillates with a frequency of \( f = 10^9 \, \text{Hz} \).

2. **Relate the Frequency of the Electromagnetic Wave to the Charged Particle**:
It is known that the frequency of the electromagnetic wave produced by an oscillating charged particle is equal to the frequency of the particle itself. Therefore, the frequency of the electromagnetic wave \( f_{wave} \) is also:
\[ f_{wave} = 10^9 \, \text{Hz} \]

3. **Calculate the Wavelength of the Electromagnetic Wave**:
The speed of electromagnetic waves in a vacuum is the speed of light, denoted as \( c \), which is approximately \( 3 \times 10^8 \, \text{m/s} \). The relationship between the speed of light, frequency, and wavelength \( \lambda \) is given by the equation:
\[ c = f_{wave} \cdot \lambda \]
Rearranging this equation to find the wavelength gives:
\[ \lambda = \frac{c}{f_{wave}} \]
Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10^9 \, \text{Hz}} = 0.3 \, \text{m} \]

4. **Determine the Type of Electromagnetic Wave**:
The wavelength calculated is \( 0.3 \, \text{m} \). To classify this wavelength, we refer to the electromagnetic spectrum. Radio waves typically have wavelengths ranging from \( 0.1 \, \text{m} \) to \( 10^6 \, \text{m} \). Since \( 0.3 \, \text{m} \) falls within this range, we conclude that the electromagnetic wave produced is a radio wave.

### Final Answers:
- The frequency of the electromagnetic wave is \( 10^9 \, \text{Hz} \).
- The wavelength of the electromagnetic wave is \( 0.3 \, \text{m} \).
- This wavelength corresponds to the radio wave range.