Atomic Structure and Nuclear Chemistry I: Foundations of Atomic Theory and Isotopes

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Atomic Structure and Nuclear Chemistry I

Introduction

This study guide covers the historical development of atomic theory, the structure of the atom, and the concept of isotopes. These foundational topics are essential for understanding modern chemistry and the behavior of elements.

Who Thought of the Atom?

Early Theories of Matter

Ancient Greek Philosophers: Proposed that all matter is composed of four elements: air, earth, fire, and water.
Democritus (~460–370 B.C.): Suggested that matter could be divided repeatedly until reaching an indivisible particle, which he called the atom (from Greek a-tomos, meaning "uncuttable").

Development of Atomic Laws

Antoine Lavoisier (1743–1794): Discovered the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.
Joseph Proust (1754–1826): Demonstrated the law of constant composition (also known as the law of definite proportions), which states that a chemical compound always contains the same proportion of elements by mass.

John Dalton and the Atomic Theory

Dalton's Atomic Theory (1808)

All matter consists of solid and indivisible atoms.
Atoms are indestructible and retain their identity in all chemical reactions.
All atoms of a given chemical element are identical in mass and in all other properties.
Different elements have different kinds of atoms; these atoms differ in mass from element to element.
Compounds consist of elements combined in small whole-number ratios.

Note: While Dalton's theory was foundational, later discoveries (such as subatomic particles and isotopes) have led to modifications of these postulates.

What's in an Atom?

Subatomic Particles

Atoms are composed of three main types of subatomic particles:

Particle	Mass (kg)	Relative Mass (u)	Charge (C)	Relative Charge	Location
Electron	9.109383 × 10−31	0.00054858	−1.602176 × 10−19	−1	Outside nucleus
Proton	1.672622 × 10−27	1.007276	+1.602176 × 10−19	+1	Nucleus
Neutron	1.674927 × 10−27	1.008665	0	0	Nucleus

Most of an atom is empty space. The nucleus is extremely small compared to the overall size of the atom but contains nearly all its mass.
The nucleus contains protons and neutrons, bound together in a region of positive charge (as demonstrated by Rutherford's gold foil experiment).
Electrons travel around the nucleus, balancing the overall charge of the atom.

Formula for Atomic Charge:

Defining an Element

Atomic Number and Mass Number

Each atom is characterized by two numbers:
- Atomic number (Z): Number of protons in the nucleus. Defines the element.
- Mass number (A): Total number of nucleons (protons + neutrons) in the nucleus.
Changing the number of protons (as in a nuclear reaction) changes the element.
Atoms of the same element can have different mass numbers; these are called isotopes.

Example: Hydrogen has three isotopes:

1H (protium): 1 proton, 0 neutrons
2H (deuterium): 1 proton, 1 neutron
3H (tritium): 1 proton, 2 neutrons

Carbon has three naturally occurring isotopes:

12C, 13C, 14C

Note: A nucleon is a general term for a proton or neutron (i.e., a particle in the nucleus).

How Useful are Isotopes?

Applications of Isotopes

Isotope ratios are used in fields such as biology, geology, paleontology, and archaeology to trace and date samples.
Forensic application: The amount of 14C in tooth enamel can be used to determine the year in which the enamel was formed, and thus estimate the year of birth (to within 1.6 years).
Atmospheric 14C levels increased during nuclear bomb testing (1955–1963) and have decreased since testing was banned. This change is recorded in biological samples.

How Can We Measure Isotopes?

Mass Spectrometry

Mass spectrometry (MS): A technique used to determine the isotopic composition of a sample by measuring the mass-to-charge ratio of ions.
The resulting mass spectrum shows the proportion of atoms belonging to each isotope in the sample.
Main difference between isotopes: Isotopes of an element have the same number of protons but different numbers of neutrons, resulting in different masses.

"Average" Samples and Atomic Mass

Weighted Average Atomic Mass

Most elements occur as mixtures of isotopes. Chemists use the weighted average atomic mass (as shown on the periodic table) to represent the element.
The average atomic mass factors in both the mass and the natural abundance of each isotope.

Formula for Average Atomic Mass:

Where:

Fractional abundance = (number of atoms of isotope) / (total number of atoms of element)

Examples

Silicon: Has three naturally occurring isotopes:
- 92.23% 28Si (27.9769 u)
- 4.67% 29Si (28.9765 u)
- 3.10% 30Si (29.9738 u)
To calculate the average atomic mass, multiply each isotopic mass by its fractional abundance and sum the results.
Gallium: Has two naturally occurring isotopes:
- 69Ga (68.926 u)
- 71Ga (70.925 u)
Given the average atomic mass (69.723 u), you can predict which isotope is more abundant and calculate the natural abundance of each isotope.

Example Calculation:

Additional info: For gallium, set up a system of equations using the average atomic mass and the sum of abundances to solve for the unknowns.