Find the wavelength of electromagnetic waves of frequency 8×`10^19` Hz in free space.

Options

A. 4×`10^(−11)m`
B. 3.7×`10^(−12)m`
C. 3.7×`10^(−10)m`
D. 37×`10^(−12)m`

Explanation

To find the wavelength of electromagnetic waves given a frequency of \(8 \times 10^{19}\) Hz, we can use the formula that relates wavelength (\(\lambda\)), frequency (\(ν\)), and the speed of light (\(c\)):

\[ c = ν \cdot λ \]

Where:
- \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8\) meters per second.
- \(ν\) is the frequency in hertz (Hz).
- \(λ\) is the wavelength in meters.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Frequency (\(ν\)) = \(8 \times 10^{19}\) Hz
- Speed of light (\(c\)) = \(3 \times 10^{8}\) m/s

2. **Rearrange the Formula to Solve for Wavelength (\(λ\)):**
\[ λ = \frac{c}{ν} \]

3. **Substitute the Values into the Formula:**
\[ λ = \frac{3 \times 10^{8} \text{ m/s}}{8 \times 10^{19} \text{ Hz}} \]

4. **Perform the Calculation:**
- First, calculate the division:
\[ λ = \frac{3}{8} \times \frac{10^{8}}{10^{19}} = 0.375 \times 10^{-11} \text{ m} \]

5. **Convert to Standard Scientific Notation:**
- \(0.375 \times 10^{-11}\) can be rewritten as:
\[ λ = 3.75 \times 10^{-12} \text{ m} \]

6. **Final Answer:**
- The wavelength of the electromagnetic waves is approximately:
\[ λ \approx 3.75 \times 10^{-12} \text{ m} \]