What is the frequency (in Hz) of light that has a wavelength of 249 nm? (Use the speed of light, c = 3.00 × 10^8 m/s.)

• A. 1.20 × 10^{15} Hz
• B. 8.36 × 10^{14} Hz
• C. 7.52 × 10^{16} Hz
• D. 2.49 × 10^{9} Hz

Answer: (A)

Verified step by step guidance

1. Identify the given values: wavelength \( \lambda = 249 \text{ nm} \) 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 \( \lambda = 249 \times 10^{-9} \text{ m} \).
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 perform the division to find the frequency in hertz (Hz).