Consider the particle$-$in$-$a$-$box problem with a box length of $5\mathrm{.}0$E$-9$ m$.$ For the $\backslash ($ n$=4\backslash )$ energy level, give one distance from the edge of the box with $\backslash ($ x$=0\backslash$mathrm$\{$~m$\}\backslash )$ is probability of finding the particle maximized? Give your answer to two significant figures.

Hint: Sketch the wavefunction. At what points is $\backslash (\backslash$psi$^\{2\}\backslash )$ maximized? What fraction of the length of this box would this be at$?$

$\backslash [$

x$=\backslash$quad $\backslash$mathrm$\{$m$\}$

$\backslash ]$

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