Find the wavelength of electromagnetic waves of frequency 5×`10^19` Hz in free space.

Options

A. 6×`10^(−12)m`
B. 6×`10^(−11)m`
C. 0.6×`10^(−12)m`
D. 6×`10^(−10)m`

Explanation

To find the wavelength of electromagnetic waves given the frequency, we can use the formula:

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

where:
- \(\lambda\) is the wavelength,
- \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8\) meters per second),
- \(\nu\) is the frequency.

### Step-by-Step Solution:

1. **Identify the given frequency**:
- The frequency \(\nu\) is given as \(5 \times 10^{19}\) Hz.

2. **Write down the speed of light**:
- The speed of light \(c\) is \(3 \times 10^8\) m/s.

3. **Substitute the values into the wavelength formula**:
\[ \lambda = \frac{c}{\nu} = \frac{3 \times 10^8 \text{ m/s}}{5 \times 10^{19} \text{ Hz}} \]

4. **Perform the division**:
- First, divide the coefficients:
\[ \frac{3}{5} = 0.6 \]
- Next, handle the powers of ten:
\[ 10^8 / 10^{19} = 10^{8 - 19} = 10^{-11} \]
- Combine these results:
\[ \lambda = 0.6 \times 10^{-11} \text{ m} = 6 \times 10^{-12} \text{ m} \]

5. **Final result**:
- The wavelength \(\lambda\) is \(6 \times 10^{-12}\) meters.

### Final Answer:
\[ \lambda = 6 \times 10^{-12} \text{ m} \]