If #nu=2.61xx10^-9*s^-1#, what is the wavelength of this light?

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Answer 1 · 2017-06-27T02:27:17

#lambda = 1.15 xx 10^8# #"nm"#

The relationship between the wavelength #lambda# and he frequency #f# of a particle is

#lambdaf = c#

Where #c# is the speed of light in vacuum, equal to precisely #299,792,458# #"m/s"#.

Recall that #1# #"Hz"# is the same as #1# #"s"^(-1)#, so the given frequency is also equal to #2.61xx10^9# #"s"^(-1)#.

Let's now plug in the known values and solve for the wavelength:

#lambda = c/f = (299792458color(white)(l)"m/"cancel("s"))/(2.61xx10^9color(white)(l)cancel("s"^(-1))) = color(red)(0.115# #color(red)("m"#

This value in nanometers is

#color(red)(0.115)cancel(color(red)("m"))((10^9color(white)(l)"nm")/(1cancel("m"))) = color(blue)(1.15 xx 10^8# #color(blue)("nm"#

Answer 2 · 2017-06-27T07:44:00

Well, #c=nuxxlambda#, where #c="speed of light,"# #m*s^-1#.

..........#nu="frequency, "s^-1#. And #lambda="wavelength"#, whose units are #m#.

And of course, #c=3.00xx10^8*m*s^-1#

And thus the product, #nuxxlambda# has units #m*s^-1# as is required for a velocity/speed.

And so #lambda=c/nu# #=# #(3.00xx10^8*m*s^-1)/(2.61xx10^9*s^-1)#

#=0.115*m#.

This is an exceptionally long wavelength.