Question

identify a set of quantum numbers for the last electron added to the titanium atom.
$n$, $l$, $m_l$, $m_s$
recall that d orbitals are one energy level behind their row and f orbitals are two energy levels behind their row.

Explanation:

Step1: Find Ti atomic number

Titanium (Ti) has atomic number 22, so 22 electrons total.

Step2: Write electron configuration

Electron configuration: $1s^22s^22p^63s^23p^64s^23d^2$

Step3: Identify last electron's orbital

Last electron fills the $3d$ orbital.

Step4: Assign principal quantum number $n$

For $3d$ orbital, $n=3$.

Step5: Assign azimuthal quantum number $l$

For $d$ orbital, $l=2$.

Step6: Assign magnetic quantum number $m_l$

For $3d^2$, the second $d$ electron can have $m_l=+1$ (or 0, -1, +2, -2; +1 is a valid choice).

Step7: Assign spin quantum number $m_s$

Electrons in separate $d$ orbitals have parallel spin, so $m_s=+\frac{1}{2}$.

Answer:

$3, 2, +1, +\frac{1}{2}$ (Note: $m_l$ can also be 0, -1, +2, -2 as valid alternatives, paired with $+\frac{1}{2}$)