Find the wavelength of electromagnetic waves of frequency 9×`10^19` Hz in free space.

Options

A. 4×`10^(−12)m`
B. 3×`10^(−12)m`
C. 4×`10^(−10)m`
D. 3×`10^(−10)m`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency (ν) = \(9 \times 10^{19}\) Hz
- Speed of light (c) = \(3 \times 10^8\) m/s

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

3. **Substitute the Values:**
Now, substitute the known values into the equation:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{9 \times 10^{19} \text{ Hz}} \]

4. **Perform the Calculation:**
\[ \lambda = \frac{3}{9} \times \frac{10^8}{10^{19}} = \frac{1}{3} \times 10^{-11} \text{ m} \]
Simplifying further:
\[ \lambda = 0.33 \times 10^{-11} \text{ m} \]
This can also be expressed as:
\[ \lambda = 3.33 \times 10^{-12} \text{ m} \]

5. **Final Answer:**
Thus, the wavelength of the electromagnetic waves is approximately:
\[ \lambda \approx 3 \times 10^{-12} \text{ m} \]