Find the wavelength of electromagnetic waves of frequency `3xx10^(12) Hz` in free space

Options

A. `10^(-4)` m
B. `10^(4) m`
C. `10^(-2) m`
D. `10^(2)m`

Explanation

To find the wavelength of electromagnetic waves with a given frequency, we can use the relationship between speed, frequency, and wavelength. The formula we will use is:

\[ \text{Wavelength} (\lambda) = \frac{\text{Speed of Light} (c)}{\text{Frequency} (f)} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Frequency \( f = 3 \times 10^{12} \, \text{Hz} \)
- Speed of light in free space \( c = 3 \times 10^{8} \, \text{m/s} \)

2. **Substitute the values into the formula**:
\[ \lambda = \frac{c}{f} = \frac{3 \times 10^{8} \, \text{m/s}}{3 \times 10^{12} \, \text{Hz}} \]

3. **Simplify the equation**:
- The \( 3 \) in the numerator and denominator cancels out:
\[ \lambda = \frac{10^{8}}{10^{12}} \, \text{m} \]

4. **Apply the laws of exponents**:
- When dividing powers of the same base, you subtract the exponents:
\[ \lambda = 10^{8 - 12} \, \text{m} = 10^{-4} \, \text{m} \]

5. **Convert to a more understandable unit (if necessary)**:
- \( 10^{-4} \, \text{m} = 0.0001 \, \text{m} = 0.1 \, \text{mm} \)

6. **Final answer**:
- The wavelength of the electromagnetic waves is \( 10^{-4} \, \text{m} \) or \( 0.1 \, \text{mm} \).

### Summary:
The wavelength of electromagnetic waves with a frequency of \( 3 \times 10^{12} \, \text{Hz} \) in free space is \( 10^{-4} \, \text{m} \).