Question

write the 4 quantum numbers of the last electron added of the following element: oxygen (o)

Explanation:

Step1: Determine the electron configuration of oxygen

Oxygen has 8 electrons. The 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 \(n = 2\).

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

For \(p\) orbitals, \(l=1\) (since \(l = 0\) 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 be \(- 1,0,1\). According to Hund's rule, in a degenerate set of orbitals (here \(2p\) orbitals), electrons are filled singly first. The last electron in \(2p\) has \(m_{l}=1\) (assuming we follow the order of filling).

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

Electrons have two possible spin values \(m_{s}=\pm\frac{1}{2}\). Since the last electron is the fourth in \(2p\) (following Hund's rule of maximum multiplicity, when filling \(p\) orbitals, the fourth electron will have a spin of \(-\frac{1}{2}\) if we consider the order of filling as per Aufbau and Hund's rules).

Answer:

\(2,1,1,-\frac{1}{2}\)