Here's how to calculate the wavelength of light given its frequency:

Understanding the Relationship

* Frequency (f): How many wave cycles pass a point in one second. Measured in Hertz (Hz).

* Wavelength (λ): The distance between two consecutive crests or troughs of a wave. Measured in meters (m).

* Speed of Light (c): The constant speed at which light travels in a vacuum. Approximately 3 x 10⁸ m/s.

The relationship between these is:

c = fλ

Solving for Wavelength

1. Rearrange the equation to solve for wavelength (λ):

λ = c / f

2. Plug in the values:

λ = (3 x 10⁸ m/s) / (7.21 x 10¹⁴ Hz)

3. Calculate:

λ ≈ 4.16 x 10^-7 m

Converting to Nanometers (nm)

Since wavelengths of light are often expressed in nanometers, let's convert:

* 1 meter (m) = 1 x 10⁹ nanometers (nm)

* λ ≈ 4.16 x 10^-7 m * (1 x 10⁹ nm / 1 m)

* λ ≈ 416 nm

Therefore, the wavelength of light with a frequency of 7.21 x 10¹⁴ Hz is approximately 416 nm.