The wavelength of a wave with frequency `10^14` Hz will be :

Options

A. `3 xx 10^(-6)` m
B. `3 xx 10^(6)` m
C. `10^(6)`m
D. None

Answer

To find the wavelength of a wave with a frequency of \(10^{14}\) Hz, we can use the formula that relates wavelength (\(\lambda\)), frequency (\(f\)), and the speed of light (\(c\)):

\[ \lambda = \frac{c}{f} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency (\(f\)) = \(10^{14}\) Hz
- Speed of light (\(c\)) = \(3 \times 10^8\) m/s (approximately)

2. **Substitute the values into the formula:**
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{10^{14} \text{ Hz}} \]

3. **Perform the division:**
- First, convert \(10^{14}\) Hz into its equivalent in seconds:
\[ 10^{14} \text{ Hz} = 10^{14} \text{ s}^{-1} \]
- Now, perform the calculation:
\[ \lambda = \frac{3 \times 10^8}{10^{14}} = 3 \times 10^{8 - 14} = 3 \times 10^{-6} \text{ m} \]

4. **Final Answer:**
- The wavelength (\(\lambda\)) is:
\[ \lambda = 3 \times 10^{-6} \text{ m} \]

### Summary:
The wavelength of a wave with a frequency of \(10^{14}\) Hz is \(3 \times 10^{-6}\) meters.