What is the frequency of a photon with a wavelength of 3,000 nm?

• A. 1.00 x 10^15 Hz
• B. 1.00 x 10^12 Hz
• C. 1.00 x 10^13 Hz
• D. 1.00 x 10^14 Hz

Answer: (C)

Verified step by step guidance

1. Identify the relationship between wavelength and frequency using the equation: \( c = \lambda \nu \), where \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s), \( \lambda \) is the wavelength, and \( \nu \) is the frequency.
2. Convert the given wavelength from nanometers to meters. Since 1 nm = \( 1 \times 10^{-9} \) m, multiply 3,000 nm by \( 1 \times 10^{-9} \) to convert it to meters.
3. Rearrange the equation \( c = \lambda \nu \) to solve for frequency \( \nu \): \( \nu = \frac{c}{\lambda} \).
4. Substitute the values for \( c \) and \( \lambda \) into the equation: \( \nu = \frac{3.00 \times 10^8 \text{ m/s}}{\text{wavelength in meters}} \).
5. Calculate the frequency \( \nu \) using the substituted values to find the answer in Hz.