Atomic Structure and Periodic Trends

Ionization energy trends

The ionization energy (IE) is the minimum energy required to remove an electron from an isolated gaseous atom or ion in its ground state, M(g) \rightarrow M^+(g) + e^-. Successive ionization energies (first, second, third and so on) refer to the removal of each subsequent electron from the species formed in the previous step. The second IE of an element is always larger than its first, because the second electron is removed from a more positively charged species. Across a period, IE generally increases, since nuclear charge rises while the added electrons enter the same shell and shield each other poorly, so the effective nuclear charge Z_{\text{eff}} felt by the valence electrons grows. Down a group, IE decreases because the valence electron lies farther from the nucleus and is shielded by more inner shells. Two exceptions must be memorized: boron has a lower IE than beryllium, and oxygen has a lower IE than nitrogen. The oxygen dip arises from electron-pair repulsion in the doubly occupied 2p orbital, while nitrogen's half-filled 2p subshell is unusually stable. The same pattern appears in the third period, where phosphorus (half-filled 3p) exceeds sulfur.

The second IE depends on which subshell the electron is removed from, so an ion with a single electron in a higher subshell can have a surprisingly low second IE. For example, the single 3p electron of \text{Si}^+ is removed more easily than a paired 3s electron of \text{Al}^+, which gives silicon the lowest second IE in the group of Al, Si, P and S.

Ionization energy rises steeply when a core electron, rather than a valence electron, must be removed. For a given species, the successive IEs of M^{n+} therefore increase with n, and the jump is largest when the electron is taken from an inner shell. Negative ions have lower removal energies than neutral atoms, which in turn have lower removal energies than cations of the same element.

Hydrogen atom energy levels

For a hydrogen-like one-electron species of nuclear charge Z, the energy of the level with principal quantum number n is E_n = -\frac{13.6\,Z^2}{n^2} eV. The energies are negative because the zero of energy corresponds to the electron removed to infinity, and the levels become less negative as n increases. The naming of excited states is a frequent source of error. The ground state is n = 1, the first excited state is n = 2, the second excited state is n = 3, and so on, so the k-th excited state corresponds to n = k + 1. Students often confuse this ordinal count with the principal quantum number itself.

When an electron falls from a higher level n_h to a lower level n_l, the emitted photon has wavenumber \bar{\nu} = R_H\left(\frac{1}{n_l^2} - \frac{1}{n_h^2}\right), where R_H is the Rydberg constant. Lines are classified into series by n_l: Lyman (n_l = 1), Balmer (n_l = 2) and Paschen (n_l = 3). Because the Rydberg constant may be given in \mathrm{m^{-1}} while the answer is requested in \mathrm{cm^{-1}}, the unit conversion (1\ \mathrm{m^{-1}} = 0.01\ \mathrm{cm^{-1}}) must be applied carefully, and rounding should be deferred to the final step.

Electronegativity periodic trends

Electronegativity is the tendency of an atom in a bond to attract the shared electron pair toward itself. The Pauling scale is the one most often used in examinations. Across a period from left to right, electronegativity increases because nuclear charge rises while atomic radius decreases. Down a group it decreases, since the bonding electrons lie farther from the nucleus. Representative Pauling values for period 3 are approximately S 2.58, P 2.19, Si 1.90 and Al 1.61, so the order is S > P > Si > Al. Metals such as aluminium have low electronegativity, while non-metals in the upper right of the periodic table are the most electronegative.

The electronegativity difference \Delta\chi between two bonded atoms controls bond polarity and ionic character, which increases with \Delta\chi. Pauling's empirical relation gives the percentage ionic character as \%\ \text{ionic} = \left[1 - e^{-(\Delta\chi)^2/4}\right] \times 100. With Pauling values of about 2.20 for H, 3.16 for Cl, 2.96 for Br and 0.93 for Na, the differences are about 0.76 for H–Br, 0.96 for H–Cl and 2.23 for Na–Cl. The bond with the smallest difference is the least ionic, so the order is H–Br < H–Cl < Na–Cl, and an ionic salt such as NaCl is essentially ionic.