A question relating to frequency i think a 10 year could do this but i cant lol

[physical101]

Homework Statement

I want to convert wavenumbers into wavelength. The wavenumber is 400cm-1 and i used the expression v=vbar*c to get the frequency in Hz to be 1.2*10^13, I also remembered to convert c into cm/s so that frequency is in its SI units (seconds). I then simply thought that I could use the expression lambda=c/v to get the answer i require and then multiply that answer by 1*10^9 to get my answer in nm instead of ms. I know the answer should be
2500nm but i get 25000nm. Why do i have this factor of 10? where did it come from?

Homework Equations

i began with vbar=400 cm-1

so then i said that

v=vbar*c

v=400*3*10^10

v=1.2*10^13 Hz

I then said that

lambda nm=(c/v)*1*10^9

lambda=(3*10^8/1.2*10^13)1*10^9

lambda = 25000 nm when it should be 2500nm or 2.5um

The Attempt at a Solution

Please see above

I know this forum is used mainly by graduates who set each other calculus based challenges but any help for a simple folk like me would be much appreciated.

 

[Stonebridge]

You would need to convert to m/s for SI units; not cm/s.

 

[physical101]

i thought that because vbar is equal to 400cm-1 that I would need to convert the speed of light to 3*10^10 so that its units become cm/s so that the cm cancel and leave the SI unit for frequency which is seconds? Is that where i went wrong?

 

[physical101]

i got it now like a fool the nm is not 1*10^-9 but 1*10^-8, please post tho if u think I am still wrong

 

[JaWiB]

1 nm = 1*10^-9 m

I get 25000nm as well (assuming wavenumber means 1/wavelength)

 

[Stonebridge]

I only read as far as the "convert to cm" and assumed that was the problem.
I don't understand why you are using the speed of light and the wave equation to do this.
If the wavenumber in 400 cm-1, that is all the information you need.
This equals 40000m-1
1/400000 = wavelength in meters
=0.000025m
=25000nm

 

[starjar]

http://imgwe.com/accessbee/27/1.png I'm[/URL] 30 and I still don't know this. It depends where your learn. You could be learning it from asia or the Caribbean. imo.