Find the wavelength of electromagnetic waves of frequency 4×`10^19` Hz in free space.

Options

A. 3.7×`10^(−12)m`
B. 7.5×`10^(−12)m`
C. 3.7×`10^(−10)m`
D. 7.5×`10^(−10)m`

Answer

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

1. **Identify the given values**:
- Frequency (ν) = \(4 \times 10^{19}\) Hz
- Speed of light (c) = \(3 \times 10^{8}\) m/s

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

3. **Substitute the values into the formula**:
\[ λ = \frac{3 \times 10^{8} \text{ m/s}}{4 \times 10^{19} \text{ Hz}} \]

4. **Calculate the wavelength**:
\[ λ = \frac{3}{4} \times \frac{10^{8}}{10^{19}} \text{ m} \]
\[ λ = 0.75 \times 10^{-11} \text{ m} \]

5. **Convert to scientific notation**:
\[ λ = 7.5 \times 10^{-12} \text{ m} \]

Thus, the wavelength of the electromagnetic waves is approximately \(7.5 \times 10^{-12}\) meters.