A beam of light has a wavelength of 7.1 × 10^2 nm. What is its frequency? (Speed of light, c = 3.00 × 10^8 m/s)

• A. 2.1 × 10^{15} Hz
• B. 4.2 × 10^{14} Hz
• C. 7.1 × 10^{16} Hz
• D. 3.0 × 10^{12} Hz

Answer: (B)

Verified step by step guidance

1. Identify the given values: wavelength \(\lambda = 7.1 \times 10^{2}\) nm and speed of light \(c = 3.00 \times 10^{8}\) m/s.
2. Convert the wavelength from nanometers to meters because the speed of light is in meters per second. Use the conversion factor \$1 \text{ nm} = 1 \times 10^{-9} \text{ m}\(, so calculate \)\lambda\( in meters as \)\lambda = 7.1 \times 10^{2} \times 10^{-9}$ 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 values of \(c\) and \(\lambda\) (in meters) into the equation and calculate the frequency \(\nu\).