Introduction to Atomic Structure, Nuclear Symbols, and Isotopic Analysis

General Atomic Geography and Structure

• Throughout the study of elements, atomic structure can be conceptualized using a relative scale analogy. If a dot represents the nucleus, the surrounding atom is the size of a stadium. The nucleus remains a tiny dot in the absolute center of that stadium.
• The nucleus contains subatomic particles known as protons and neutrons. Protons are characterized by their quality of having a positive electrical charge. Neutrons are also located within the nucleus and have specific mass attributes.
• Electrons are located outside the nucleus and carry a negative electrical charge. In a natural, or neutral, state, the number of positive charges (protons) equals the number of negative charges (electrons).

Fundamental Identity: The Proton and Atomic Number

• Each element is identified and defined by its unique number of protons in its nucleus. This value is known as the atomic number ($Z$).
• The atomic number functions as a label for elements on the periodic table, much like a seat number in a theater. Hydrogen is assigned seat number one because it contains exactly one proton in its nucleus.
• As scientists discover new elements, they are assigned higher atomic numbers and placed into the periodic table. Currently, 118 elements have been discovered.

Nomenclature of Elements: Names and Symbols

• A chemical symbol is used to represent an element rather than writing out its full name. Each element is represented by one capital letter or one capital letter paired with one lowercase letter.
• Elements like Hydrogen are represented by a single capital letter ($H$). Often, the capital letter is the first letter in the English name of the element, such as Aluminum ($Al$), which uses the first two letters.
• Elements like Helium ($He$) use a capital letter and a lowercase letter to distinguish them from others.
• Certain elements use symbols derived from Latin rather than English, particularly heavy metals. Examples include:
  • Gold ($Au$).
  • Silver ($Ag$).
  • Mercury ($Hg$).

The Nuclear Symbol and Isotopic Notation

• The nuclear symbol is a representation used to determine subatomic particles (protons and neutrons) which can be released or formed during nuclear energy processes that break atoms apart.
• A nuclear symbol consists of three primary pieces of information:
  • The Element Symbol ($X$): Found on the periodic table.
  • The Atomic Number ($Z$): Written as the lower number on the symbol, representing the number of protons.
  • The Mass Number ($A$): Written as the upper number on the symbol, representing the sum of protons and neutrons.
• On most periodic tables, the atomic number is the smaller whole number, and the elements are organized sequentially according to this number (1, 2, 3, etc.).

Mathematical Determination of Subatomic Particles

• The total mass of an atom is the sum of its protons and neutrons. This is expressed by the sum equation: $\text{Mass Number (A)} = \text{Proton Number} + \text{Neutron Number}$.
• For calculation purposes, the mass of one proton is approximately one atomic mass unit ($1\,AMU$ or $ATM$), and the mass of one neutron is also approximately one atomic mass unit.
• To find the number of neutrons, subtract the atomic number from the mass number: $\text{Neutrons} = A - Z$.
• Example using Scandium ($Sc$):
  • Atomic Number specified as 21.
  • Mass Number specified as 46.
  • Calculation: $46 - 21 = 25\,neutrons$.

Concepts of Isotopes

• Isotopes are atoms of the same element that share the same number of protons but have different mass numbers because they contain different numbers of neutrons.
• In nature, elements often exist as a family of isotopes. For example, Chlorine ($Cl$) has two isotopes with masses of approximately $35\,AMU$ and $37\,AMU$.
• Isotope Rules:
  • The element symbol, atomic number, and number of protons remain the same for all isotopes of a specific element.
  • The mass number and the number of neutrons are always different between isotopes.
• Isotopes are often identified by writing the element name or symbol followed by a dash and the mass number (e.g., $H-1$, $H-2$, or $H-3$).

The Hydrogen Isotope Family

• Hydrogen exists in three main isotopic forms, all of which are colorless gases:
  • Protium ($H-1$): Contains one proton and zero neutrons in the nucleus.
  • Deuterium ($H-2$ or $D$): Contains one proton and one neutron. Molecularly written as $D_2$. It is used in specialized lamps and scientific instruments.
  • Tritium ($H-3$): The heaviest isotope, containing one proton and two neutrons. It is the isotope with the largest mass number in the Hydrogen family.

Forensic Case Study: Stable Isotope Analysis

• Stable isotope analysis is used in forensic investigations to determine the geographical origin of substances like the illegal drug cocaine.
• Cocaine is a compound containing carbon, hydrogen, nitrogen, and oxygen. The isotopic ratios of Oxygen ($O-16$ vs. $O-18$) and Hydrogen ($H-1$ vs. $H-2$) vary based on temperature and humidity in specific regions.
• By analyzing the percentage of these isotopes, investigators can determine if a sample originated from Southeast Asia or Colombia. For instance, a sample from Southeast Asia might have specific percentage footprints that differ significantly from a sample with $96\%$ of one isotope and $4\%$ of another from Colombia.

Ionic Species: Cations and Anions

• Ions are charged atoms formed when an atom gains or loses electrons during chemical reactions or bonding.
• An atoms starts in a neutral state with a charge of zero.
• Anion: A negatively charged ion formed when an atom gains electrons. Anions are named by adding the suffix "-ide" to the root name of the element (e.g., Fluorine becomes Fluoride; Oxygen becomes Oxide).
• Cation: A positively charged ion formed when an atom loses electrons. Metals on the left side of the periodic table, such as Sodium ($Na$) and Calcium ($Ca$), typically form cations.
• Ions possess significantly different physical and chemical properties compared to their neutral parent atoms. For example, neutral Sodium is an explosive, soft metal kept away from air, while the Sodium ion ($Na^+$) is stable and safe for consumption in compounds like sodium chloride.

Qualitative Calculation of Ion Electrons

• To determine the number of electrons in an ion, use the atomic number as the starting point and adjust for the charge.
• Positive Charge: Subtract the charge number from the atomic number (loss of electrons). For Aluminum ($Al^{3+}$, atomic number 13), the calculation is $13 - 3 = 10\,electrons$.
• Negative Charge: Add the charge number to the atomic number (gain of electrons). For Selenium ($Se^{3-}$, atomic number 34), the calculation is $34 + 3 = 37\,electrons$.

Experimental Instrumentation in Chemistry

• UV-Vis Absorption Spectrophotometer: Used in hospital laboratories to identify substances like blood proteins and dry substances. The lamps used in these instruments, such as those containing Deuterium gas, can cost between $1,000 and $2,000.
• Mass Spectrometer: An instrument used to determine the exact mass of different isotopes present in a sample.

Questions & Discussion

Q: What is the number of protons and neutrons for Nitrogen with a mass of 15?

• The atomic number for Nitrogen ($N$) is 7, meaning it has 7 protons. The neutrons are calculated as $15 - 7 = 8$.

Q: How many protons, neutrons, and electrons are in Phosphorus-35 (P-35)?

• Allison and Addison identified that Phosphorus has an atomic number of 15, so it has 15 protons. The neutrons are calculated using the given mass number: $35 - 15 = 20$. It has 15 electrons as it is neutral.

Q: For Copper-62 ($Cu^{2+}$), what are the subatomic particle counts?

• Benjamin determined that Copper has 29 protons (atomic number 29). The neutrons are $62 - 29 = 33$. Because the charge is $2+$, the atom has lost two electrons: $29 - 2 = 27\,electrons$.

Q: What are the values for Selenium-76 ($Se^{3-}$)?

• Alexandra identified the atomic number for Selenium as 34, meaning 34 protons. The neutrons are calculated as $76 - 34 = 42$. With a $3-$ charge, indicating the gain of three electrons, the total electron count is $34 + 3 = 37$.