ACS General Chemistry

This section covers the structure of the atom: subatomic particles, the historical and quantum mechanical models, quantum numbers, electron configurations of atoms and ions, isotopes and average atomic mass, the interaction of light with atoms, and periodic trends. ACS items ask students to identify valid quantum number sets, write or interpret configurations (including transition-metal ions and magnetic behavior), calculate photon energies and wavelengths, and rank elements or ions by radius, ionization energy, and electronegativity.

The atom is the fundamental unit of matter: all matter consists of atoms, and the arrangement of an atom's electrons determines how it bonds and reacts. Nearly every topic in general chemistry builds on the model of the atom developed in this chapter.

Subatomic Particles

Atoms contain three primary subatomic particles. Protons (charge +1) and neutrons (no charge) reside in the nucleus; electrons (charge −1) occupy the space surrounding the nucleus in regions called orbitals. The nucleus is extremely small and dense and contains virtually all of the atom's mass. Protons and neutrons each have a mass of approximately 1 atomic mass unit (amu); an electron's mass is negligible, about 1/1836 the mass of a proton.

Particle	Symbol	RelativeCharge	Mass(amu)	Location
Proton	p⁺	+1	10073(≈1) .	Nucleus
Neutron	n⁰	0	10087(≈1) .	Nucleus
Electron	e⁻	−1	0000549(≈0) .	Orbitalsaroundthenucleus

Atomic Models

The model of the atom evolved as experiments revealed new structure. The modern quantum mechanical model replaces fixed paths with orbitals: regions of space where there is a high probability of finding an electron. Because electrons behave as waves (de Broglie wavelength λ = h/mv) and their position and momentum cannot both be known exactly (Heisenberg uncertainty principle), only probability distributions can be described. Each electron's state is specified by four quantum numbers.

Model	KeyIdea	EvidenceorLimitation
Daltonatomictheory	Atomsareindivisiblespheres;atomsofoneelement	Explainedthelawsofdefiniteandmultiple
	are identical; compounds form in whole-number	proportions;didnotrecognizesubatomic
	ratios	particles
Thomsonplumpudding	Electronsembeddedinadiffusepositivematrix	Cathode-ray experiments showed the electron
Rutherfordnuclearmodel	Atiny dense positivenucleuswithelectrons , , surroundingit;theatomismostlyemptyspace	existsandisnegative 1 Gold -foil experiment: most alpha particles passedthrough afewdeflectedsharply ,

Developmentoftheatomicmodel(Continued)

Model	KeyIdea	EvidenceorLimitation
Bohrmodel	Electronsoccupyquantizedorbitswithspecific	Explainedthehydrogenlinespectrum;failsfor
	energies	atomswithmorethanoneelectron
Quantummechanical	Electronsdescribedbywavefunctions(orbitals)	Currentmodel;givesprobabilities notpaths ,
model	andfourquantumnumbers

Quantum Numbers

QuantumNumber	AllowedValues	WhatItDescribes
Principal n ,	1 2 3 , , , …	Mainenergylevel(shell)andorbitalsize;highernmeansgreater
		averagedistancefromthenucleusandhigherenergy
Angularmomentum l ,	0 to (n − 1)	Orbital shape (subshell): l = 0 is s (spherical) , 1 is p (dumbbell) , 2 is d
		(cloverleaf) 3isf(complex) ,
Magnetic ml ,	−l to +l including 0 ,	Orbital orientation in space; for l = 1 , ml = −1 , 0 , +1 (the p x, p y, p z
		orbitals)
Spin m , s	+½or−½	Electron spin (spin-up or spin-down)

Shelln	Subshells(l)	OrbitalsperSubshell	Orbitals(n²)	Maxe⁻(2n²)
1	1s	1	1	2
2	2s 2p ,	1 3 ,	4	8
3	3s 3p 3d , ,	1 3 5 , ,	9	18
4	4s 4p 4d 4f , , ,	1 3 5 7 , , ,	16	32

A subshell with quantum number l has 2l + 1 orbitals and holds up to 2(2l + 1) electrons: s = 2, p = 6, d = 10, f = 14. An orbital has n − 1 total nodes, of which l are angular nodes and n − l − 1 are radial nodes.

Invalid quantum number sets are a favorite item. l must be less than n (so 2d and 1p do not exist), and |ml| cannot exceed l. The set n = 3, l = 2, ml = −2, ms = +½ is valid (a 3d electron); n = 2, l = 2 is invalid; n = 3, l = 1, ml = +2 is invalid.

Electron Configuration

An electron configuration describes how electrons are distributed among orbitals. Three principles govern the filling of orbitals in the ground state.

Follows increasing n + l; for equal n + l, the lower n fills first (4s before 3d, 5s before 4d). The periodic table's blocks give the same order: s block (groups 1–2), d block (groups 3–12), p block (groups 13–18), f block (lanthanides and actinides).

Exampleground-Stateconfigurations

Element	FullConfi guration	Noble-Gas Notation
Hydrogen(H)	1s¹	1s¹
Carbon(C)	1s²2s²2p²	[He]2s²2p²
Sodium(Na)	1s²2s²2p⁶3s¹	[Ne]3s¹
Iron(Fe)	1s²2s²2p⁶3s²3p⁶4s²3d⁶	[Ar]4s²3d⁶

Noble gas notation uses the preceding noble gas in brackets as a core and writes only the electrons beyond it. Valence electrons are those in the highest occupied shell (for main-group elements, the ns and np electrons); they determine chemical behavior. In an orbital diagram, carbon's two 2p electrons occupy separate 2p orbitals with parallel spins (Hund's rule), and nitrogen's three 2p electrons are all unpaired.

Exceptions to Expected Configurations

Chromium and copper have unexpected configurations because half-filled (d⁵) and completely filled (d¹⁰) d subshells are especially stable, and the 4s and 3d energies are very close. Chromium is [Ar] 4s¹ 3d⁵ rather than [Ar] 4s² 3d⁴; copper is [Ar] 4s¹ 3d¹⁰ rather than [Ar] 4s² 3d⁹. The elements below them follow the same pattern: molybdenum is [Kr] 5s¹ 4d⁵ and silver is [Kr] 5s¹ 4d¹⁰.

Configurations of Ions

For main-group ions, add or remove electrons in the valence shell; most reach a noble-gas configuration (Na⁺ = [Ne]; Cl⁻ = [Ar]; S²⁻ = [Ar]; Al³⁺ = [Ne]). For transition-metal cations, the ns electrons are removed before the (n − 1)d electrons, even though ns fills first. Once 3d orbitals are occupied, 4s lies higher in energy and its electrons are lost first.

Transition-Metalionconfigurations

Transition-Metalionconfigurations(Continued)

Species	Confi guration	Unpairede⁻	MagneticBehavior
Fe³⁺	[Ar]3d⁵	5	Paramagnetic
Cu⁺	[Ar]3d¹⁰	0	Diamagnetic
Zn²⁺	[Ar]3d¹⁰	0	Diamagnetic
Mn²⁺	[Ar]3d⁵	5	Paramagnetic

A species with one or more unpaired electrons is paramagnetic and is weakly attracted into a magnetic field; the more unpaired electrons, the stronger the attraction. A species in which all electrons are paired is diamagnetic and is weakly repelled by a magnetic field. Oxygen atoms (2p⁴, two unpaired) are paramagnetic; Ne, Zn, and Zn²⁺ are diamagnetic. Any atom or ion with an odd number of electrons must be paramagnetic.

"Last in, first out" does not apply to transition metals. Fe²⁺ is [Ar] 3d⁶, not [Ar] 4s² 3d⁴. To count unpaired electrons, place the d electrons in five boxes using Hund's rule: d¹–d⁵ are all unpaired; d⁶ has 4 unpaired, d⁷ has 3, d⁸ has 2, d⁹ has 1, and d¹⁰ has none.

Atomic Number and Mass Number