Question

A beam of visible light has a frequency of 4.5x10^14 Hz. What is the wavelength of this light? What color is this light?

Answer 1

The wavelength is about 666.2 nm.

The color is red.

Step-by-step explanation:

Recall the relationship between frequency and wavelength:

`\displaystyle c = \lambda \\u`

Solve for wavelength λ:

`\displaystyle \lambda = (c)/(\\u)`

Substitute and evaluate. Note that 1 Hz = 1 s⁻¹:

`\displaystyle \begin{aligned} \lambda & = \frac{(2.998* 10^(8) \text{ m/s})}{(4.5* 10^(14) \text{ /s})} \cdot \frac{1* 10^9\text{ nm}}{1\text{ m}} \\ \\ & = 666.2 \text{ nm}\end{aligned}`

Therefore, the wavelength of the light is about 666.2 nm.

This corresponds with the red region of the visible spectrum.