What is the wavelength in nanometers of light with a frequency of 7.8 × 10^{15} Hz? (Speed of light c = 3.00 × 10^{8} m/s)

• A. 38 nm
• B. 2.6 nm
• C. 390 nm
• D. 256 nm

Answer: (A)

Verified step by step guidance

1. Recall the relationship between the speed of light (c), frequency (\( \nu \)), and wavelength (\( \lambda \)) given by the equation: \[ c = \lambda \times \nu \]
2. Rearrange the equation to solve for wavelength (\( \lambda \)): \[ \lambda = \frac{c}{\nu} \]
3. Substitute the given values into the equation: \[ \lambda = \frac{3.00 \times 10^{8} \text{ m/s}}{7.8 \times 10^{15} \text{ Hz}} \]
4. Calculate the wavelength in meters by performing the division, keeping track of the powers of ten carefully.
5. Convert the wavelength from meters to nanometers by multiplying by \( 10^{9} \) since 1 meter = \( 10^{9} \) nanometers: \[ \lambda_{\text{nm}} = \lambda_{\text{m}} \times 10^{9} \]