The wavelength of some violet light is 420.0 nm. What is the frequency of this violet light? (Speed of light, c = 3.00 × 10^8 m/s)

• A. 1.26 × 10^{12} Hz
• B. 4.20 × 10^{15} Hz
• C. 3.00 × 10^{8} Hz
• D. 7.14 × 10^{14} Hz

Answer: (D)

Verified step by step guidance

1. Identify the given values: wavelength \( \lambda = 420.0 \text{ nm} \) and speed of light \( c = 3.00 \times 10^{8} \text{ m/s} \).
2. Convert the wavelength from nanometers to meters because the speed of light is in meters per second. Use the conversion \( 1 \text{ nm} = 1 \times 10^{-9} \text{ m} \), so \( \lambda = 420.0 \times 10^{-9} \text{ m} \).
3. Recall the relationship between the speed of light, wavelength, and frequency: \[ c = \lambda \times \nu \] where \( \nu \) is the frequency.
4. Rearrange the formula to solve for frequency \( \nu \): \[ \nu = \frac{c}{\lambda} \].
5. Substitute the values of \( c \) and \( \lambda \) into the equation and calculate \( \nu \) to find the frequency of the violet light.