= Solution
Use the common <ionization continuum> consisting of a divalent <calcium ion> and a free <electron> as the upper reference, with the <singly ionized calcium> ground state $4s\,{}^2S_{1/2}$ at zero <energy>. The resonance <doublet (spectroscopy)> is
$$
\boxed{4p\,{}^2P_{3/2}\to4s\,{}^2S_{1/2}\ (393.4\ \mathrm{nm}),\qquad
4p\,{}^2P_{1/2}\to4s\,{}^2S_{1/2}\ (396.9\ \mathrm{nm}).}
$$
The higher-$J$ P component is higher in <energy> because its emission to the common lower level has the shorter <wavelength>. The full series is $np\,{}^2P_{1/2,3/2}\to4s\,{}^2S_{1/2}$. As $n\to\infty$, its two upper levels approach the same continuum, so the ground-state <ionization energy> is approximately $hc/(104.4\ \mathrm{nm})=11.88$ eV.
The second doublet has a common \b[upper] S level and two lower P levels:
$$
\boxed{5s\,{}^2S_{1/2}\to4p\,{}^2P_{3/2}\ (373.7\ \mathrm{nm}),\qquad
5s\,{}^2S_{1/2}\to4p\,{}^2P_{1/2}\ (370.6\ \mathrm{nm}).}
$$
Both combinations put $5s\,{}^2S_{1/2}$ near $6.47$ eV above the ground state. The series is $ns\,{}^2S_{1/2}\to4p\,{}^2P_{1/2,3/2}$ with $n\geq5$. Its two limits measure the <ionization energy> \b[from each lower P level], giving slightly different limit <wavelengths> near 142 nm, not two unrelated continua. From the rounded <wavelengths>, $E(4p_{1/2})\simeq3.124$ eV and $E(4p_{3/2})\simeq3.152$ eV, leaving roughly $8.74$ eV to the same continuum. The tabulated level ordering and labels independently agree with these assignments.<Energy Levels of Singly Ionized Calcium (Ca II) by National Institute of Standards and Technology>[4s,4p and5s entries and Ca III continuum limit]{ref}
The quoted <wavelengths> and limits are rounded; air and vacuum conventions also matter for precision spectroscopy. They justify a labelled schematic and the approximate <energy> differences, not an artificial claim of exact closure at every printed decimal.
\Image[/past-exam-of-the-quantum-atomic-and-molecular-physics-course-of-the-university-of-oxford/2016-calcium-ion-series-levels.png]
{title=Common-continuum assignments of the Ca+ doublets and infrared triplet}
{description=Original schematic showing every first-doublet and infrared-triplet transition and the three approximate series limits. Fine splittings are visually enlarged; vertical positions are not a precision energy scale.}
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