# Calculations with wavelength and frequency

## Key Questions

• If you note the units you are using, it becomes easier.

You have $\frac{1}{\text{s}}$, and oftentimes with wavelength, you want to convert to $\text{nm}$ which is UV-Vis range ($\text{200~700 nm}$), and is often of spectral interest.

What you want to do is:

$\frac{1}{\text{s" -> 1/"m" -> "m" -> "nm}}$

Conversion factors are extremely useful, and one easy one to remember is the speed of light, which is about $\text{3" xx 10^8 "m/s}$.

1/(1/cancel("s") * cancel("s")/"m") = "m"

And finally, we can convert to $\text{nm}$:

10^9 "nm" = "1 m" -> "conversion factor: "(10^9 "nm")/("1 m")

cancel"m" * (10^9 "nm")/(1 cancel"m")

Thus, overall, you just have:

$\textcolor{b l u e}{\text{nm") = 1/(1/cancel("s") * cancel("s")/(3xx10^8 cancel"m")) * (10^9 "nm")/(1 cancel"m}}$

$= \textcolor{b l u e}{\frac{1}{1 \text{/"cancel("s"))*3xx10^8 cancel("m")"/"cancel("s") xx (10^9 "nm")/(1 cancel"m}}}$