Find the wavelength of electromagnetic waves of frequency 7×`10^19` Hz in free space.

Options

A. 4×`10^(−12)m`
B. 6×`10^(−12)m`
C. 5×`10^(−12)m`
D. 44×`10^(−12)m`

Explanation

To find the wavelength of electromagnetic waves given the frequency, we can use the formula that relates frequency (ν), wavelength (λ), and the speed of light (C):

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Frequency (ν) = \(7 \times 10^{19}\) Hz
- Speed of light (C) = \(3 \times 10^{8}\) m/s

2. **Use the Formula**:
The relationship between frequency, wavelength, and speed of light is given by:
\[ \nu = \frac{C}{\lambda} \]
Rearranging this formula to find the wavelength (λ):
\[ \lambda = \frac{C}{\nu} \]

3. **Substitute the Values**:
Now, substitute the values of C and ν into the equation:
\[ \lambda = \frac{3 \times 10^{8} \text{ m/s}}{7 \times 10^{19} \text{ Hz}} \]

4. **Calculate the Wavelength**:
Performing the division:
\[ \lambda = \frac{3}{7} \times 10^{8 - 19} \text{ m} = \frac{3}{7} \times 10^{-11} \text{ m} \]
Now, calculate \(\frac{3}{7}\):
\[ \frac{3}{7} \approx 0.4286 \]
Therefore,
\[ \lambda \approx 0.4286 \times 10^{-11} \text{ m} \approx 4.286 \times 10^{-12} \text{ m} \]

5. **Final Result**:
Rounding this value gives:
\[ \lambda \approx 4 \times 10^{-12} \text{ m} \]

### Conclusion:
The wavelength of the electromagnetic waves with a frequency of \(7 \times 10^{19}\) Hz in free space is approximately \(4 \times 10^{-12}\) meters.