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

1 Answer
Jun 30, 2017

#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.