A hydrogen atom in the $\backslash ($ n$=7\backslash )$ state decays to the $\backslash ($ n$=4\backslash )$ state. What is the wavelength of the photon that the hydrogen atom emits? Use $\backslash ($ h c$=1240\backslash$mathrm$\{$~nm$\}\backslash )$ eV$.$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$nm$\}\backslash )$

While in the first excited state, a hydrogen atom is illuminated by various wavelengths of light. What happens to the hydrogen atom when illuminated by each wavelength?

$486\mathrm{.}3$ nm $?$

$491\mathrm{.}3$ nm $?$ jumps to $\backslash ($ n$=4\backslash )$ state

$315\mathrm{.}9$ nm $?$

Note: For a transition between bound states $($finite $\backslash ($ n $\backslash ))$ you need to match the correct wavelength to about $8$ significant figures. For this problem, treat a transition as happening if the wavelength is within $1\mathrm{.}0$ nm $.$ WHAT IS THE ANSWER FOR THE LAST TWO THAT ARE WRONG?