Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# Converting and dealing with inverse centimeters(cm-1),nanometer(nm-1),seconds(s-1)?

I assume you are referring to interconverting between lambda, nu, and tildenu, or something like that? I say this because lambda is typically wavelength in "nm", nu is typically frequency in "s"^-1, and tildenu means energy in wavenumbers ("cm"^-1). If you want "nm"^(-1), just reciprocate "nm".

There are four possibilities for conversions that I could cover:

1. lambda->nu
2. nu->tildenu
3. nu->lambda
4. tildenu->nu

However, recognize that if you can do 1 and 2, you have done 3 and 4 backwards, and if you can do 1 and 2 consecutively, you can go straight from lambda to tildenu (same with 3 and 4 but tildenu to lambda). So, I will only show 1 and 2.

• lambda->nu

Suppose we have lambda = 600nm for yellow light and we want its frequency in s^-1.

What we want is to convert from a unit of length to a unit of reciprocal time, which requires something that has "length"/"time" units... The speed of light works great here, and it's about 3xx10^8 "m/s". Therefore:

1. Reciprocate the wavelength
2. Convert to "m"
3. Multiply by the speed of light

overbrace((1/(600 cancel("nm"))))^(lambda)xx((10^9 cancel("nm"))/(1 cancel("m")))xx(3xx10^8 cancel("m")/"s") = underbrace(color(blue)(5.bar55xx10^(-3) "s"^-1))_(nu)

• nu->tildenu

This is fairly straightforward. We have 1/"s" and want 1/"cm". Suppose we have a frequency of 6xx10^(-3) "s"^-1.

1. Divide by the speed of light
2. Convert to "cm"

overbrace((6xx10^(-3) 1/cancel("s")))^(nu)xx(cancel("s")/(3xx10^8 cancel("m")))xx((1 cancel("m"))/(100 "cm")) = underbrace(color(blue)(2xx10^(-13) "cm"^(-1)))_(tildenu)

LEARN MORE EFFECTIVELY AND GET BETTER GRADES!