Question

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?

Answer 1

The frequency of light with wavelength 406 nm can be found using the equation ν = c / λ, and the wavelength of radiation with a frequency of 2.09 × 109 Hz can be determined by rearranging that equation to λ = c / ν.

Step-by-step explanation:

To calculate the frequency of light with a given wavelength, we can use the equation c = λν, where c is the speed of light (approximately 3 × 108 m/s), λ is the wavelength, and ν is the frequency. For light with a wavelength of 406 nm (which is 406 x 10-9 meters), the frequency can be calculated as ν = c / λ.

To find the wavelength given the frequency, we rearrange the equation to λ = c / ν. So, the wavelength of radiation with a frequency of 2.09 × 109 Hz is calculated by dividing the speed of light by the frequency.

Answer 2

1. frequency = 7.39 * 10¹⁴ Hz

2. wavelength = 1.44 * 10⁸ nm

Step-by-step 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