Give the set of four quantum numbers that could represent the electron lost to form the k ion from the k atom

There are four quantum numbers, the principal number (n), angular momentum number (l), magnetic quantum number (ml) and spin number (ms). Let me discuss each along the way.

The quantum number refer to the outermost shell of the atom where valence electrons reside. To do this, perform first the electric configuration. For K⁺, the number of electrons is 1 electron lesser than the neutral K. This is equal to  19 - 1 = 18. Follow the guidelines shown in the first picture. These are the number of electrons each subshell can hold:

s = 1 electron
p = 6 electrons
d = 20 electrons
f = 28 electrons

The electronic configuration for K+ is shown in the second picture. There are a total of 18 electrons. Let's focus on the last subshell where the last electron was: in the 3p subshell. The quantum number n =3 because it is at energy level 3. The quantum number l is 1. The guideline for this is that s =0, p=1. d=2. f=3. Next, the ml is 0. Just number the boxes with the middle being 0. Lastly, the ml is -1 because a downward spin is -1 (while an upward spin is +1).

Thus, the five quantum numbers for the last electron in K+ is 3, 1, 0 and -1.