Question

write the 4 quantum numbers of the last electron added of the following element; oxygen (o)
2, 2, 2, -1/2
2, 1, 1, -1/2
2, 1, 0, -1/2

Explanation:

Step1: Determine the electron configuration of Oxygen

Oxygen has an atomic number of 8. Its electron configuration is \(1s^{2}2s^{2}2p^{4}\). The last electron is added to the \(2p\) orbital.

Step2: Identify the principal quantum number (\(n\))

For the \(2p\) orbital, the principal quantum number \(n = 2\) (since it is in the second energy level).

Step3: Identify the azimuthal quantum number (\(l\))

For \(p\) orbitals, the azimuthal quantum number \(l=1\) (\(l = 0\) for \(s\), \(l = 1\) for \(p\), \(l = 2\) for \(d\), etc.).

Step4: Identify the magnetic quantum number (\(m_{l}\))

For \(l = 1\), \(m_{l}\) can have values \(- 1,0,1\). According to Hund's rule, when filling \(p\) orbitals (with 3 degenerate orbitals), electrons first occupy each orbital singly with parallel spins. For the fourth electron in \(2p\) (after three singly - occupied \(2p\) orbitals with spin \(+\frac{1}{2}\)), the fourth electron will pair up. Let's assume it pairs in the \(m_{l}=1\) orbital (but in a more accurate sense, for the last - added electron in \(2p^{4}\), if we follow the Aufbau principle and Hund's rule, when we start filling the \(2p\) orbitals: first three electrons have \(m_{l}=-1,0,1\) with \(s =+\frac{1}{2}\), and the fourth electron will have \(m_{l} = 1\) (for example, but actually, the magnetic quantum number for the last - added electron can be any of \(-1,0,1\) depending on the orbital it pairs in. However, in a more standard approach for \(2p\) electrons, when we consider the order of filling, the last electron has \(m_{l}=1\))

Step5: Identify the spin quantum number (\(m_{s}\))

Since it is pairing, the spin quantum number \(m_{s}=-\frac{1}{2}\) (opposite to the spin of the first electron in that orbital)

Answer:

\(n = 2\), \(l = 1\), \(m_{l}=1\), \(m_{s}=-\frac{1}{2}\) which corresponds to \(2,1,1,-\frac{1}{2}\) (the second option in the given choices)