Quantum numbers and electron configurations
Every electron in an atom has a complete "address": which main energy level it is in, which type of sublevel, which orbital exactly, and which way it spins. That address is the set of four quantum numbers. The rules for filling these addresses explain the shape of the periodic table.
The four quantum numbers
Shells, subshells and orbitals are labeled with quantum numbers. The numbers $n$ and $l$ are the key vocabulary you need most (for example, $3p$ means $n = 3$, $l = 1$). The other two, $m_l$ and $m_s$, are mainly used to count orbitals and to say that an orbital holds two electrons of opposite spin. How do these labels describe the different states available to an electron within one main energy level?
The Pauli exclusion principle
Filling orbitals: the Aufbau principle and Hund's rule
Liquid oxygen sticks to a strong magnet, while liquid nitrogen ($Z = 7$) does not. Neon ($Z = 10$) has all its electrons paired, so it is not attracted by a magnet either. By what rules are orbitals filled, and why do some atoms keep unpaired electrons?
Phosphorus is an essential nonmetallic element with atomic number Z = 15. a) Write the electron configuration of the phosphorus atom in its ground state according to the…
Phosphorus is an essential nonmetallic element with atomic number Z = 15.
- a) Write the electron configuration of the phosphorus atom in its ground state according to the Aufbau principle or Moeller diagram.
- b) State how many unpaired electrons it has in its valence shell according to Hund's rule of maximum multiplicity, and deduce whether the neutral ground-state atom is paramagnetic or diamagnetic.
Consider the neutral carbon atom (Z = 6), whose complete electron configuration begins with the sublevel $1s^2\,2s^2$ and ends with two electrons in the 2p sublevel. The…
Consider the neutral carbon atom (Z = 6), whose complete electron configuration begins with the sublevel $1s^2\,2s^2$ and ends with two electrons in the 2p sublevel. The following diagram shows three possible arrangements (A, B, and C) for the two electrons in the three degenerate 2p orbitals:
- a) Identify which of the three options corresponds to the ground state of carbon, justifying your choice using the quantum rules for filling orbitals.
- b) Analyze in detail which quantum principle or rule is violated in each of the two remaining options.
Ions and transition metals
Magnetic measurements show that $\mathrm{Fe}^{3+}$ has five unpaired electrons and $\mathrm{Fe}^{2+}$ has four. The $4s$ sublevel fills before $3d$ when building the neutral atom, so which sublevel loses electrons first when a positive ion forms?
Iron is a transition element with atomic number Z = 26. a) Write the electron configuration of the neutral iron atom in its ground state and justify why, when it ionizes…
Iron is a transition element with atomic number Z = 26.
- a) Write the electron configuration of the neutral iron atom in its ground state and justify why, when it ionizes to form the cation $\mathrm{Fe}^{2+}$, it loses the 4s electrons before those of the 3d sublevel.
- b) Write the electron configuration of the cation $\mathrm{Fe}^{3+}$ and determine, giving reasons, which of the two species, $\mathrm{Fe}^{2+}$ or $\mathrm{Fe}^{3+}$, will have the greater number of unpaired electrons and, consequently, stronger paramagnetic behavior.
Chromium (Z = 24) and copper (Z = 29) show recognized anomalies with respect to the usual mnemonic rule of the Madelung diagram. a) Write the ground-state electron…
Chromium (Z = 24) and copper (Z = 29) show recognized anomalies with respect to the usual mnemonic rule of the Madelung diagram.
- a) Write the ground-state electron configuration predicted by the standard Madelung filling order for $\mathrm{Cr}$ and $\mathrm{Cu}$, and compare each with the experimentally verified actual configuration.
- b) Justify the quantum and energetic cause of these anomalous configurations, based on the stability associated with half-filled or completely filled sublevels and on the small energy difference between the 4s and 3d orbitals.
Back to the start: the periodic table has blocks that are 2, 6, 10 and 14 columns wide because these match the maximum number of electrons in the $s$ ($2 \cdot 1 = 2$), $p$ ($2 \cdot 3 = 6$), $d$ ($2 \cdot 5 = 10$) and $f$ ($2 \cdot 7 = 14$) sublevels.