What is an example of a wavelength calculations practice problem?

1 Answer
Truong-Son N.
Nov 3, 2015

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.

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