1. What is the frequency of light having a wavelength of 406 nm?

2. What is the wavelength (in nm) of radiation having a frequency of 2.09 * 109 Hz?

1. frequency = 7.39 * 10¹⁴ Hz

2. wavelength = 1.44 * 10⁸ nm

Explanation:

The speed, frequency and wavelength of waves are related by the formula;

speed = wavelength * frequency

1. wavelength of light = 406 nm = 4.06 * 10⁻⁷ m

speed of light is a constant = 3.0 * 10⁸ m/s

From the formula above, frequency = speed / wavelength

therefore, frequency = (3.0 * 10⁸ m/s) / 4.06 * 10⁻⁷ m

frequency = 7.39 * 10¹⁴ Hz

2. From the equation above, wavelength = speed/frequency

speed of radiation = 3.0 * 10⁸ m/s

frequency = 2.09 * 10⁹ Hz or 2.09 * 10⁹ s⁻¹

therefore, wavelength = (3.0 * 10⁸ m/s) / 2.09 * 10⁹ s⁻¹

wavelength = 1.44 * 10⁸ nm