The frequency of a wave light is `1.0 xx 10^(6)sec^(-1)`. The wave length for this wave is

Options

A. `3 xx 10^(4)cm`
B. `3 xx 10^(-4)cm`
C. `6 xx 10^(4)cm`
D. `6 xx 10^(6)cm`

Explanation

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

\[ c = \lambda \cdot \nu \]

Where:
- \( c \) is the speed of light, approximately \( 3.0 \times 10^8 \) meters per second.
- \( \lambda \) is the wavelength in meters.
- \( \nu \) is the frequency in hertz (Hz), which is given as \( 1.0 \times 10^6 \, \text{sec}^{-1} \).

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency (ν) = \( 1.0 \times 10^6 \, \text{sec}^{-1} \)
- Speed of light (c) = \( 3.0 \times 10^8 \, \text{m/s} \)

2. **Rearrange the formula to solve for wavelength (λ):**
\[ \lambda = \frac{c}{\nu} \]

3. **Substitute the known values into the formula:**
\[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{1.0 \times 10^6 \, \text{sec}^{-1}} \]

4. **Perform the calculation:**
\[ \lambda = 3.0 \times 10^8 \div 1.0 \times 10^6 = 3.0 \times 10^{8-6} = 3.0 \times 10^2 \, \text{meters} \]
\[ \lambda = 300 \, \text{meters} \]

5. **Convert the wavelength from meters to centimeters (if needed):**
- Since \( 1 \, \text{meter} = 100 \, \text{centimeters} \):
\[ \lambda = 300 \, \text{meters} \times 100 \, \text{cm/m} = 30000 \, \text{cm} \]
\[ \lambda = 3.0 \times 10^4 \, \text{cm} \]

### Final Answer:
The wavelength of the wave is \( \lambda = 3.0 \times 10^4 \, \text{cm} \).

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