A charged particle oscillates about its mean equilibrium position with a frequency of `10^(9) Hz`. The wavelength (in m ) of ELECTROMAGNETIC WAVES produced will be

Answer

To solve the problem of finding the wavelength of electromagnetic waves produced by a charged particle oscillating with a frequency of \(10^9\) Hz, we can follow these steps:

### Step 1: Understand the relationship between wavelength, frequency, and speed of light
The wavelength (\(\lambda\)) of electromagnetic waves is related to the speed of light (\(c\)) and the frequency (\(f\)) by the formula:
\[ \lambda = \frac{c}{f} \]

### Step 2: Identify the values for \(c\) and \(f\)
From the problem:
- The speed of light, \(c\), is approximately \(3 \times 10^8\) m/s.
- The frequency, \(f\), is given as \(10^9\) Hz.

### Step 3: Substitute the values into the formula
Now we can substitute the known values into the wavelength formula:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{10^9 \text{ Hz}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ \lambda = \frac{3 \times 10^8}{10^9} = 0.3 \text{ m} \]

### Step 5: State the final answer
Thus, the wavelength of the electromagnetic waves produced is:
\[ \lambda = 0.3 \text{ m} \]

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