Question #fd5ae

1 Answer
Feb 2, 2017

#5.9 * 10^(-7)"m"#

Explanation:

The thing to remember about wavelength, #lamda#, and frequency, #nu#, is that they have an inverse relationship as described by the equation

#color(blue)(ul(color(black)(nu * lamda = c)))#

Here #c# is the speed of light in a vacuum, usually given as #3 * 10^8"m s"^(-1)#.

This inverse relationship basically means that if you multiply the frequency and the wavelength of a given electromagnetic wave, the result will always be equal to the speed of light.

You can rearrange the equation to solve for #lamda#

#nu * lamda = c implies lamda = c/(nu)#

Now, keep in mind that the frequency of yellow light is given to you in hertz, #"Hz"#, which as you know are equivalent to #"s"^(-1)#.

You will thus have

#lamda = (3 * 10^8"m" color(red)(cancel(color(black)("s"^(-1)))))/(5.1 * 10^(14) color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(5.9 * 10^(-7)"m")))#

The answer is rounded to two sig figs because the speed of light is a constant, which implies that you can use it with as many significant figures as you want.