Atoms and Elements: Foundations of Atomic Theory and the Periodic Table

Atoms and Elements

Historical Thoughts on Matter

The concept of matter has evolved over centuries, beginning with philosophical inquiry and advancing through scientific experimentation.

• Ancient Greek Philosophy: The Greeks questioned whether matter could be divided endlessly. Their experiments suggested substances retained their properties upon division, leading to the idea of matter as a continuous, infinitely divisible entity.

Atom as a Solid Sphere

John Dalton's atomic theory marked a pivotal shift in understanding matter as composed of discrete units.

• Dalton's Hypothesis (1807): Matter consists of atoms, which are indivisible solid spheres.

• Law of Multiple Proportions: Atoms combine in simple, whole-number ratios to form compounds.

• Experimental Evidence: Einstein and Perrin confirmed the existence of atoms via Brownian motion in the early 1900s.

The Law of Multiple Proportions

This law describes how elements combine in different compounds.

• Definition: When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

• Example: Carbon dioxide (CO2) and carbon monoxide (CO):

  • Mass oxygen to 1 g carbon in CO2: 2.67 g

  • Mass oxygen to 1 g carbon in CO: 1.33 g

  • Ratio: $\frac{2.67}{1.33} = 2$

Discovery of the Electron

The electron was discovered through experiments with cathode ray tubes.

• Cathode Ray Tube (CRT): High voltage between electrodes produces a discharge (current).

• Changing the gas or pressure affects the discharge, indicating the presence of a fundamental particle.

The Charge/Mass Ratio of the Electron

J.J. Thompson measured the charge-to-mass ratio of the electron using the CRT.

• Method: Deflection of cathode rays in electric and magnetic fields.

• Result: $\frac{e}{m} = 1.76 \times 10^8 \text{ C/g}$

The "Oil Drop" Experiment

Robert Millikan determined the charge of the electron using the oil drop apparatus.

• Method: Oil droplets were suspended in an electric field, balancing gravitational and electrical forces.

• Result: Charge of electron found to be multiples of $-1.6 \times 10^{-19}$ C.

• Calculation: $\frac{e}{m} = \frac{-1.6 \times 10^{-19} \text{ C}}{1.76 \times 10^8 \text{ C/g}} = 9.1 \times 10^{-28} \text{ g}$

Rutherford’s Gold Foil Experiment

Ernest Rutherford’s experiment provided evidence for the nuclear model of the atom.

• Method: Alpha particles were directed at a thin gold foil.

• Expected: Most particles would pass through with minor deflection.

• Actual Result: Some particles bounced back, indicating a dense, positively charged nucleus.

The Development of Atomic Theory

Atomic theory evolved through several models:

• Continuum Model: Matter is infinitely divisible.

• Solid Sphere Model: Atoms are indivisible spheres.

• Plum Pudding Model: Electrons embedded in a positively charged matrix.

• Nuclear Model: Dense nucleus with electrons in surrounding space.

The Nuclear Atom

The modern atomic model describes a dense nucleus surrounded by electrons.

• Nucleus: Contains protons and neutrons.

• Electrons: Occupy a large volume around the nucleus; most of the atom is empty space.

• Protons: Equal but opposite charge to electrons; about 2000 times heavier.

• Neutrons: Contribute to atomic mass and act as nuclear "glue".

Subatomic Particles

Atoms are composed of three main subatomic particles:

Particle	Mass (kg)	Mass (amu)	Charge (relative)	Charge (C)
Proton	1.67262 × 10-27	1.00727	+1	+1.60218 × 10-19
Neutron	1.67493 × 10-27	1.00866	0	0
Electron	0.00091 × 10-27	0.00055	-1	-1.60218 × 10-19

The Atom

An atom is the smallest unit of an element, retaining its chemical properties.

• Scale: Atoms are extremely small (e.g., carbon atom diameter ≈ 3 × 10-10 m).

• Mole: Due to their small size, atoms are counted in moles for practical purposes.

• Visualization: Atoms are often represented as color-coded spheres.

Definition of the Elements

Elements are defined by the number of protons in their nuclei.

• Atomic Number (Z): Number of protons.

• Mass Number (A): Sum of protons and neutrons.

• Symbol: Chemical symbol represents the element (e.g., $^{12}_{6}\text{C}$ for carbon).

Definition of Isotopes

Isotopes are atoms of the same element with different numbers of neutrons.

• Same chemical properties, different mass numbers.

• Natural abundance: The relative proportion of each isotope in nature is constant.

Symbol	Number of Protons	Number of Neutrons	Mass Number (A)	Natural Abundance (%)
He-20, or 20Ne	10	10	20	90.48
He-21, or 21Ne	10	11	21	0.27
He-22, or 22Ne	10	12	22	9.25

The Periodic Table

The periodic table organizes elements by increasing atomic number and groups elements with similar properties.

• Periods: Horizontal rows.

• Groups: Vertical columns.

• Main-group elements: Groups 1, 2, and 13-18.

• Transition elements: Groups 3-12.

The Element Groups

Elements are classified into groups with shared properties.

Group	Name	Elements
1A	Alkali metals	Li, Na, K, Rb, Cs, Fr
2A	Alkaline earth metals	Be, Mg, Ca, Sr, Ba, Ra
6A	Chalcogens	O, S, Se, Te, Po
7A	Halogens	F, Cl, Br, I, At
8A	Noble gases	He, Ne, Ar, Kr, Xe, Rn

Metals

Metals occupy the lower-left and middle of the periodic table and share characteristic properties.

• Properties:

  • Good conductors of heat and electricity

  • Malleable (can be pounded into sheets)

  • Ductile (can be drawn into wires)

  • Often shiny

  • Tend to lose electrons in chemical reactions

• Examples: Sodium, magnesium, calcium, copper, lithium, lead

Nonmetals

Nonmetals are found on the upper-right side of the periodic table and display varied properties.

• Properties:

  • Poor conductors of heat and electricity

  • Not ductile or malleable

  • Gain electrons in chemical reactions

• States at Room Temperature:

  • Solids: C, P, S, Se, I

  • Liquid: Br

  • Gases: H, He, N, O, F, Ne, Cl, Ar, Kr, Xe, Rn

• Examples: Oxygen, carbon, nitrogen, iodine

Metalloids

Metalloids, or semimetals, have properties intermediate between metals and nonmetals.

• Located along the zigzag line dividing metals and nonmetals.

• Exhibit mixed properties; some are semiconductors.

• Examples: Boron, silicon, germanium, arsenic, antimony, tellurium, argon, tennessine

Periodic Table Sections

The periodic table is divided into main-group elements, transition elements, and inner transition elements.

• Main-group elements: Groups 1, 2, and 13-18

• Transition elements: Groups 3-12

Periodic Table: Rows and Columns

Understanding the organization of the periodic table is essential for predicting element properties.

• Groups (families): Vertical columns, numbered 1-18 (or 1A-8A, 1B-8B)

• Periods: Horizontal rows, numbered 1-7

Group: Noble Gases

Noble gases are found in group 8A and are characterized by their lack of chemical reactivity.

• Properties: Chemically stable, do not form compounds easily

• Examples: Helium, neon, argon, krypton, xenon

Group: Alkali Metals

Alkali metals are highly reactive metals found in group 1A.

• Properties: React vigorously with water, soft, shiny

• Examples: Lithium, sodium, potassium, rubidium, cesium

Group: Alkaline Earth Metals

Alkaline earth metals are found in group 2A and are less reactive than alkali metals.

• Properties: Fairly reactive, form basic oxides

• Examples: Magnesium, calcium, strontium, barium

Group: Halogens

Halogens are very reactive nonmetals found in group 7A.

• Properties: Form salts with metals, exist in various physical states

• Examples: Fluorine (gas), chlorine (gas), bromine (liquid), iodine (solid)

Charges on Elemental Ions

Elements tend to form ions by gaining or losing electrons to achieve noble gas electron configurations.

• Main-group metals: Lose electrons to form cations.

• Main-group nonmetals: Gain electrons to form anions.

Group	Common Ion Charge
1A	+1
2A	+2
6A	-2
7A	-1
8A	0

Calculating Atomic Mass

The atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes.

• Formula: $\text{Atomic mass} = \sum (\text{fraction of isotope n}) \times (\text{mass of isotope n})$

• Example: Chlorine atomic mass is calculated from the abundance and mass of its isotopes.

The Mole: A Chemist’s “Dozen”

The mole is a counting unit used to express amounts of a chemical substance.

• Definition: 1 mole = $6.02214076 \times 10^{23}$ particles (Avogadro's constant)

• Analogy: Like a dozen (12 objects), a mole is a large number for counting atoms, molecules, etc.

Converting Moles and Atoms

Conversions between moles and number of atoms use Avogadro's constant as a conversion factor.

• Conversion factors: $1 \text{ mol atoms} = 6.022 \times 10^{23} \text{ atoms}$ $6.022 \times 10^{23} \text{ atoms} = 1 \text{ mol atoms}$

Converting Mass and Amount (# Moles)

To determine the number of atoms in a sample, mass is converted to moles using molar mass, then to atoms using Avogadro's constant.

• Molar mass: The mass of 1 mole of atoms of an element (g/mol), numerically equal to atomic mass in amu.

• Example:

  • 26.98 g aluminum = 1 mol aluminum = $6.022 \times 10^{23}$ Al atoms

  • 12.01 g carbon = 1 mol carbon = $6.022 \times 10^{23}$ C atoms

  • 4.003 g helium = 1 mol helium = $6.022 \times 10^{23}$ He atoms

Mass, Mole, Atoms Calculations

Counting atoms in a sample involves a stepwise conversion:

• Obtain mass of sample (g)

• Convert mass to moles using molar mass (g/mol)

• Convert moles to number of atoms using Avogadro's constant

Conceptual Plan:

• g element → mol element → number of atoms

Formula:

• $\text{Number of atoms} = \frac{\text{mass of sample (g)}}{\text{molar mass (g/mol)}} \times 6.022 \times 10^{23}$