Question

A certain red light has a wavelength of 680 nm. What is the frequency of the light?

Answer 1

`f = 4.4 xx 10^14` `"s"^-1`

Explanation:

We're asked to convert a given wavelength of a wave to its frequency.

We can use the equation

`lambdaf = c`

where

• `lambda` (the lowercase Greek letter lambda) is the wavelength of the wave, in meters

• `f` is the frequency of the wave, in inverse seconds (`"s"`) or hertz (`"Hz"`)

• `c` is the speed of light in vacuum, precisely `299,792,458` `"m/s"`

Since our wavelength must be in units of `"m"`, we'll convert from nanometers to meters, knowing that `1` `"m"` `= 10^9` `"nm"`:

`680cancel("nm")((1color(white)(l)"m")/(10^9cancel("nm"))) = color(red)(6.80 xx 10^-7` `color(red)("m"`

Plugging in known values to the equation and solving for `f`, we have

`f = c/lambda`

`f = (299792458(cancel("m")/"s"))/(6.80xx10^-7cancel("m")) = color(blue)(4.4 xx 10^14` `color(blue)("s"^-1) = color(blue)(4.4 xx 10^14` `color(blue)("Hz"`

rounded to `2` significant figures.