Question

What is an example of a wavelength calculations practice problem?

Answer 1

Chances are, if you work with wavelengths `lambda`, you are probably going to see Planck's constant `h`, so let's try one of those problems.

Try calculating the energy of a single photon of a particular wavelength.

`E_"photon" = hnu = (hc)/lambda`

... if its wavelength is red (let's say the wavelength was `"600 nm"`). The speed of light is about `2.998xx10^8 "m/s"` and `h = 6.626xx10^(-34) "J"cdot"s"`.

Here's a hint for your units: `"J" = "kg"*"m"^2"/s"^2`. What do you need to do to get to `"J"` by operating with `"J"cdot"s"`, `"m"`, and `"nm"^(-1)`?

You should get `color(blue)(3.31079xx10^(-19)"J")`.

(If you get `3.31079xx10^(-17)"J"`, check your wavelength. `"600 nm" ne 6xx10^(-9) "m"`.)

CHALLENGE: See if you can convert the energy here from `"J"` to `"cm"^(-1)`. Hint: `c = 3xx10^10 "cm/s"`, and consider the only equation given above.