The frequency of a green light is `6 xx 10^(14)Hz`. Its wavelength is

Options

A. 500nm
B. 5nm
C. 5000nm
D. none of these

Explanation

To find the wavelength of green light given its frequency, we can use the relationship between frequency (ν), wavelength (λ), and the speed of light (c). The formula is:

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

Where:
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \nu \) is the frequency (given as \( 6 \times 10^{14} \) Hz),
- \( \lambda \) is the wavelength in meters.

### Step-by-Step Solution:

1. **Write down the formula**:
\[ c = \nu \cdot \lambda \]

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

3. **Substitute the known values into the equation**:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{6 \times 10^{14} \text{ Hz}} \]

4. **Perform the division**:
- First, divide the coefficients:
\[ \frac{3}{6} = 0.5 \]
- Next, subtract the exponents (using the property of exponents):
\[ 10^8 / 10^{14} = 10^{8-14} = 10^{-6} \]
- Combine these results:
\[ \lambda = 0.5 \times 10^{-6} \text{ m} \]

5. **Convert to a more standard form**:
- Rewrite \( 0.5 \times 10^{-6} \) as:
\[ 5 \times 10^{-7} \text{ m} \]

6. **Convert to nanometers**:
- Since \( 1 \text{ nm} = 10^{-9} \text{ m} \):
\[ 5 \times 10^{-7} \text{ m} = 500 \text{ nm} \]

### Final Answer:
The wavelength of the green light is \( 500 \text{ nm} \).