In your research on new solid$-$state devices, you are studying a solid$-$state structure that can be modeled accurately as an electron in a one$-$dimensional infinite potential well $($box$)$ of width $\backslash ($ L $\backslash ).$ In one of your experiments, electromagnetic radiation is absorbed in transitions in which the initial state is the $\backslash ($ n$=1\backslash )$ ground state. You measure that light of frequency $\backslash ($ f$=9\mathrm{.}6\backslash$times $10^\{14\}\backslash$mathrm$\{$~Hz$\}\backslash )$ is absorbed and that the next higher absorbed frequency is $\backslash (18\mathrm{.}0\backslash$times $10^\{14\}\backslash$mathrm$\{$~Hz$\}\backslash ).$

Part A

Part B

Part C

What is the width $\backslash ($ L $\backslash )$ of the potential well?

Express your answer with the appropriate units.

Correct

Part D

What is the longest wavelength in air of electromagnetic wave that can be absorbed by an electron if it is initially in the $\backslash (\backslash$boldsymbol$\{$n$\}=1\backslash )$ state?

Express your answer with the appropriate units.