If a photon's wavelength is 663 nm, what is its frequency? (Speed of light c = 3.00 × 10^8 m/s)

• A. 1.99 × 10^{12} Hz
• B. 2.21 × 10^{15} Hz
• C. 6.63 × 10^{13} Hz
• D. 4.53 × 10^{14} Hz

Answer: (D)

Verified step by step guidance

1. Identify the given values: wavelength \( \lambda = 663 \text{ nm} \) 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 \( \lambda = 663 \times 10^{-9} \text{ m} \).
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: \[ \nu = \frac{c}{\lambda} \].
5. Substitute the known values into the equation and calculate the frequency \( \nu \) (do not compute the final number here, just set up the expression): \[ \nu = \frac{3.00 \times 10^{8} \text{ m/s}}{663 \times 10^{-9} \text{ m}} \].