Atomic Structure and Nuclear Chemistry: Foundations and Applications

Atomic Structure and Nuclear Chemistry

Introduction

This study guide covers the foundational concepts of atomic structure and nuclear chemistry, including the historical development of atomic theory, the structure of atoms, and the significance of isotopes. These topics are essential for understanding the nature of matter and its transformations in chemical reactions.

Who Thought of the Atom?

Historical Development of Atomic Theory

• Ancient Greek Philosophers: Early thinkers proposed that all matter was composed of four elements: air, earth, fire, and water. This idea dominated scientific thought for centuries.

• Democritus (~460–370 B.C.): Disagreed with the four-element theory, suggesting that matter could be subdivided until reaching an indivisible particle called the atom (from Greek atomos, meaning "uncuttable").

• Antoine Lavoisier (1743–1794): Formulated the law of conservation of mass, stating that mass is neither created nor destroyed in chemical reactions.

• 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.

Example: Water (H2O) always contains hydrogen and oxygen in a mass ratio of approximately 1:8.

John Dalton's Atomic Theory

Postulates of Dalton's Atomic Theory (1808)

• All matter consists of solid and indivisible atoms.

• Atoms are indestructible and retain their identity in chemical reactions.

• All atoms of a given chemical element are identical in mass and other properties.

• Atoms of different elements differ in mass and other properties.

• Compounds consist of elements combined in small whole-number ratios.

Modern Modifications: While Dalton's theory laid the groundwork for modern chemistry, subsequent discoveries (such as subatomic particles and isotopes) have led to modifications of these postulates.

Example: The existence of isotopes shows that atoms of the same element can have different masses.

What's in an Atom?

Subatomic Particles

Atoms are composed of three fundamental subatomic particles:

Particle	Mass (kg)	Charge (C)	Location
Electron	9.109382 × 10−31	−1.602176 × 10−19	Outside nucleus
Proton	1.672622 × 10−27	+1.602176 × 10−19	Nucleus
Neutron	1.674927 × 10−27	0	Nucleus

• Most of an atom is empty space. The nucleus is extremely small compared to the overall size of the atom, but contains most of its mass.

• Nucleus: Contains protons and neutrons, bound together in a region of positive charge (as demonstrated by Rutherford's gold foil experiment).

• Electrons: Move around the nucleus in defined regions, balancing the overall charge of the atom.

Atomic Charge Formula:

$\text{Charge} = \text{Number of protons} - \text{Number of electrons}$

Defining an Element

Atomic Number and Mass Number

• Atomic Number (Z): The number of protons in the nucleus; defines the element.

• Mass Number (A): The total number of nucleons (protons + neutrons) in the nucleus.

Example: For carbon-12: $A = 12$, $Z = 6$

Changing the number of protons (as in nuclear reactions) changes the element itself.

Isotopes

• Atoms of the same element can have different mass numbers due to varying numbers of neutrons. These are called isotopes.

• Most elements have more than one naturally occurring isotope.

Isotope	Symbol	Protons	Neutrons
Hydrogen-1	$^1_1\text{H}$	1	0
Hydrogen-2 (Deuterium)	$^2_1\text{H}$	1	1
Hydrogen-3 (Tritium)	$^3_1\text{H}$	1	2
Carbon-12	$^{12}_6\text{C}$	6	6
Carbon-13	$^{13}_6\text{C}$	6	7
Carbon-14	$^{14}_6\text{C}$	6	8

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

Applications and Importance of Isotopes

Uses of Isotopes

• Isotope ratios are used in fields such as biology, geology, paleontology, and archaeology to trace and date samples.

• Forensic applications: For example, atmospheric $^{14}\text{C}$ levels increased during nuclear bomb testing (1955–1963) and decreased after testing was banned. The amount of $^{14}\text{C}$ in tooth enamel can be used to determine the year of birth within 1.6 years.

Example: Radiocarbon dating uses the decay of $^{14}\text{C}$ to estimate the age of organic materials.

Measuring Isotopes and Atomic Mass

Mass Spectrometry

• Mass spectrometry is a technique used to determine the proportion of atoms belonging to each isotope in a sample.

• The resulting spectrum shows the relative abundance of each isotope.

Average Atomic Mass

• Most elements exist as mixtures of isotopes. The atomic mass shown on the periodic table is the weighted average of all naturally occurring isotopes.

• The average atomic mass factors in both the mass and abundance of each isotope.

Formula for Average Atomic Mass:

$\text{Average atomic mass} = \sum (\text{fractional abundance of isotope}) \times (\text{mass of isotope})$

Example Calculation:

• Silicon has three naturally occurring isotopes:

  • 92.23% $^{28}\text{Si}$ (27.9769 u)

  • 4.67% $^{29}\text{Si}$ (28.9765 u)

  • 3.10% $^{30}\text{Si}$ (29.9738 u)

  Average atomic mass: $0.9223 \times 27.9769 + 0.0467 \times 28.9765 + 0.0310 \times 29.9738$

Additional info: The concept of weighted averages is crucial for interpreting atomic masses and understanding the natural abundance of isotopes.