Atomic Structure and Periodic Table Notes

Nucleus and Electron Cloud: A Visual Overview

• The atom consists of a small positively charged nucleus in the middle and a surrounding cloud of negatively charged electrons.

  • Nucleus contains protons (positive) and neutrons (neutral).

  • Outside, electrons zip around, forming a diffuse negative cloud.

  • The nucleus is extremely small compared to the overall size of the atom: mass is concentrated in the nucleus, while the electrons occupy most of the space.

  • For scale, an angstrom is a common unit: $1\,\text{Å} = 1.0 \times 10^{-10}\text{ m}$. In everyday terms, the atom is on the order of angstroms across; the electron cloud is vast compared to the tiny nucleus.

  • A common analogy: the nucleus is like a dot; the electron cloud is like a large, diffuse halo around it.

• Relative sizes and scale analogies used in teaching:

  • If the atom is the size of a Michigan Stadium, the nucleus is like a fly in the middle of the field.

  • If the electron cloud were scaled to human dimensions, the electrons would be imagined as a large cloud surrounding the nucleus.

• Key takeaway: most of the atom’s volume is empty space occupied by the electron cloud; mass is concentrated in the tiny nucleus.

Subatomic Particles: Charge, Z, A, and N

• Subatomic particles and their charges:

  • Protons: positive charge; reside in the nucleus; define the atomic number Z.

  • Neutrons: neutral; reside in the nucleus; contribute to mass but not charge.

  • Electrons: negative charge; arranged around the nucleus in an electron cloud; define the atom’s charge state.

• Important quantities:

  • Atomic number Z = number of protons in the nucleus.

  • Mass number A = Z + N, where N = number of neutrons. Hence, N = A − Z.

  • Electron count in a neutral atom: number of electrons E = Z (since protons balance electrons for neutrality).

  • In symbols, Z is the letter used for atomic number; it appears in several notations and texts.

• Isotopes and mass:

  • Atoms can share the same Z (same number of protons) but have different numbers of neutrons, giving different mass numbers A. These are isotopes.

  • Iso- means "same" (same number of protons).

  • Neutrons affect mass, not charge, so isotopes have the same charge but different masses.

• Isotope notation and examples:

  • The standard notation is $^{A}_{Z}X$ where X is the element symbol, Z is the atomic number, and A is the mass number.

  • Example for hydrogen isotopes:

  • Protium: $^{1}_{1}H$ (A = 1, Z = 1, N = 0).

  • Deuterium: $^{2}_{1}H$ (A = 2, Z = 1, N = 1).

  • Tritium: $^{3}_{1}H$ (A = 3, Z = 1, N = 2).

• Hydrogens’ different isotopes and mass numbers:

  • Mass number A = Z + N, thus for hydrogen (Z = 1):

  • Protium: N = 0, A = 1.

  • Deuterium: N = 1, A = 2.

  • Tritium: N = 2, A = 3.

• A radiology-related example (isotopes):

  • Technetium-99 (Tc-99) is mentioned as a clinically used isotope.

  • To describe a neutral Tc-99 atom:

  • Protons: $Z = 43$ (technetium’s atomic number).

  • Neutrons: from the mass number, $N = A - Z = 99 - 43 = 56$.

  • Electrons in a neutral Tc-99 atom: $E = Z = 43$.

  • Summary for Tc-99 in neutral state: protons = 43, neutrons = 56, electrons = 43.

  • This illustrates how Z, A, and N determine the subatomic composition of isotopes.

• Summary concept about isotopes:

  • Isotopes have the same atomic number Z (same protons) and thus the same chemical properties under many conditions, but different neutron counts lead to different masses and often different stability or radioactivity.

Atomic Weight and Molecular Weight

• Atomic weight (often called atomic mass) vs molecular weight:

  • Atomic weight of an element is the average mass of its atoms, weighted by the relative abundance of its isotopes.

  • This average is not necessarily an integer because it reflects natural isotope mixtures.

  • The atomic weight is around, but not exactly equal to, the sum of integer counts of protons and neutrons for a single isotope.

  • The unit used for atomic and molecular weights is the atomic mass unit, abbreviated as amu (also written as u).

• Formula for atomic weight (conceptual):

  • If an element has isotopes i with mass numbers Ai and fractional abundances fi (where (\sumi fi = 1)), then
    $\text{Atomic weight} = \sum<em>i f</em>i A_i.$

  • This is a weighted average over all isotopes of the element.

• Molecular weight (molar mass) for a compound:

  • The molecular weight is the sum of the atomic weights of all atoms in the molecule.

  • Example: water, H$2$O: $M(\mathrm{H</em>2O}) = 2\times M(\mathrm{H}) + M(\mathrm{O}).$

  • If we take the approximate atomic masses (in amu): $M(\mathrm{H}) \approx 1$, $M(\mathrm{O}) \approx 16$, then
    $M(\mathrm{H_2O}) = 2\times 1 + 16 = 18\,\text{amu}.$

  • Glucose, C$6$H${12}$O$_6$ (approximately):
    $M = 6\times 12 + 12\times 1 + 6\times 16 = 180\,\text{amu}.$

  • Note: these weights are used descriptively in biochemistry; this is often termed descriptive biochemistry rather than a quantitative problem set in this context.

• Relationship to isotopes:

  • Elements with multiple isotopes have atomic weights that are not whole numbers because the isotopes contribute different masses according to their abundances.

• Terminology recap:

  • Atomic weight (average mass of element, weighted by isotope abundances)

  • Mass number A (integer, A = Z + N)

  • Atomic number Z (number of protons, defines identity of the element)

  • Number of neutrons N = A − Z

  • Molecular weight (sum of atomic weights for all atoms in a molecule)

Carbon Isotopes and Isotopic Differences

• Two common carbon isotopes: Carbon-12 and Carbon-14.

  • Both have the same atomic number Z = 6 (same protons).

  • They have different mass numbers A: 12 and 14, due to different numbers of neutrons.

  • For neutral isotopes of carbon, the number of electrons is the same (E = Z = 6).

  • The neutrons differ: N = A − Z, so for C-12: N = 6, for C-14: N = 8.

  • In brief: identical protons and electrons, different neutrons, different mass numbers.

• Takeaway:

  • Isotopes are identified by their mass number A (and Z), but their chemical behavior is largely governed by the number of protons (Z) and electrons, particularly the valence electrons for main-group elements.

Electron Shells, Subshells, and Orbitals

• Basic picture:

  • Electrons occupy energy shells around the nucleus. Each electron’s energy increases with distance from the nucleus.

  • Farther electrons are higher energy (more unstable) and more available to participate in reactions.

  • Closer electrons are lower energy (more stable).

• Addressing an electron’s location (the four-part address, focusing on two):

  • Shell: principal quantum number $n$ (n = 1, 2, 3, …). The closer the shell (smaller $n$), the lower the energy.

  • Subshell: within a shell, the shape is described by subshells named $s, p, d, f$. The shapes and names follow historical conventions.

  • Orbitals: each subshell splits into orbitals, and each orbital can hold two electrons with opposite spins.

  • Spin: electrons in the same orbital must have opposite spins (up & down), though we focus mainly on shells and subshells here.

• Subshell capacities mentioned:

  • $s$ subshell: 2 electrons total (1 orbital).

  • $p$ subshell: 6 electrons total (3 orbitals).

  • $d$ subshell: 10 electrons total (5 orbitals).

  • $f$ subshell: 14 electrons total (7 orbitals).

• Shell-by-shell buildup (as described):

  • The first shell ( $n = 1$ ) has only $s$ subshell: up to 2 electrons.

  • The second shell ( $n = 2$ ) has $s$ and $p$ subshells: up to 2 + 6 = 8 electrons.

  • The third shell ( $n = 3$ ) has $s$, $p$, and $d$ subshells: up to 2 + 6 + 10 = 18 electrons.

  • The fourth shell ( $n = 4$ ) adds the $f$ subshells: up to 2 + 6 + 10 + 14 = 32 electrons.

  • As shells get larger, more subshells appear, allowing more electrons per shell.

• Degeneracy concept:

  • Within a given shell, the orbitals are of the same energy (degenerate) before considering small differences due to subshell energies.

  • Hence, within a shell (before filling order considerations), all orbitals in that shell are treated as having the same energy level for a simplified view.

• Connection to the periodic table:

  • The periodic table’s arrangement reflects the electron structure, especially valence electrons, not just raw atomic numbers.

Valence Electrons and the Periodic Table

• Valence electrons and the valence shell:

  • The valence shell is the outermost energy shell that contains electrons.

  • The electrons in the valence shell are called valence electrons; they largely determine chemical reactivity and bonding.

• Main-group elements and their valence electrons:

  • For main-group elements, the valence shell can hold a maximum of eight electrons (two in the $s$ subshell and six in the $p$ subshell).

  • This leads to a typical valence electron count ranging from 1 to 8, depending on the group.

  • Group patterns (old labeling and intuition):

  • 1A (Group 1): 1 valence electron.

  • 2A (Group 2): 2 valence electrons.

  • 4A (Group 14): 4 valence electrons (example: carbon).

  • 6A (Group 16): 6 valence electrons (example: oxygen).

  • Helium (rarely discussed with a “valence” context): has 2 electrons in the first shell but is not considered in the same way as the other main-group elements.

• How to read the main groups on the periodic table:

  • The Roman numerals (I–VIII) or the “A” designation lines up with groups that have the same valence electron counts.

  • The bottom line highlights the periodic trends in valence behavior, which correlates with chemical properties.

• Example concept: calcium (Ca) and strontium (Sr) both have two valence electrons because they sit in the same group (2A). This makes them chemically similar, especially in comparison to potassium (K) in group 1A, which has one valence electron.

• Quick practice question addressed in the discussion:

  • Do calcium and potassium or calcium and magnesium have more similar chemistry? Answer: magnesium, because it shares the same group (valence electron count of 2).

• Overall takeaway:

  • The periodic table encodes electronic structure information: the number of valence electrons (and which shell is the valence shell) largely determines chemical properties and bonding behavior.

Periodic Table Organization: Rows (Periods), Columns (Groups), and Blocks

• How the table is organized conceptually:

  • Elements are arranged in order of increasing atomic number (Z).

  • Rows are called periods; there are seven.

  • Columns are called groups or families; there are 18.

  • Some group names are presented using Roman numerals or the A/B system; the main groups (often called the “A” groups) are especially emphasized.

• Bottom and top numbers on the periodic table:

  • The top number for each element is the atomic number Z (number of protons).

  • The bottom number is the atomic weight (or relative atomic mass), which is a weighted average of isotopes’ masses.

  • The bottom numbers reflect isotope abundances and are not exact counts of protons, neutrons, and electrons for a single atom.

• The main blocks on the table (context for electron filling, per the lecture):

  • s-block: two columns; contains the first two groups (including hydrogen and the alkaline metals).

  • p-block: six columns; contains groups 13–18 (main-group elements plus noble gases).

  • d-block: ten columns; transition metals (not the focus of the current emphasis but acknowledged).

  • f-block: fourteen elements; the lanthanides and actinides (also acknowledged but not the focus here).

• Focus on the main groups:

  • The main groups (the “s” and “p” blocks) are where the majority of the elements of interest in this course reside (e.g., H, C, N, O, etc.).

  • These elements account for the majority of atoms in biological molecules and common chemistry.

• Practical note on reading the table:

  • When studying, you’ll often reference the main groups to infer valence electron counts and likely chemical behavior without calculating electron configurations for every element.

Oxygen: A Quick Electronic Structure Reference

• Oxygen (O) in the periodic table:

  • Atomic number Z = 8; neutral atom contains 8 electrons (for a neutral atom, E = Z).

  • These 8 electrons occupy energy shells around the nucleus—the first shell and the second shell contain the electrons.

  • The electrons farther from the nucleus are higher energy and more reactive; the electrons closer to the nucleus are lower energy and more stable.

• General idea of an electron’s “address” in the atom (revisited):

  • The shell (n) determines energy level.

  • The subshell (s, p, d, f) indicates shape and capacity; within a subshell, orbitals hold two electrons with opposite spins.

• Oxygen in terms of valence:

  • Oxygen is in the 2nd period and the 16th group (6A); thus it has 6 valence electrons in its outer shell (the 2nd shell) and will seek to gain two more electrons to complete its valence shell to eight electrons.

  • This aligns with its typical role in forming two bonds and achieving a stable octet in many compounds.

Practical Example: Calcium and Strontium Valence Electrons

• Calcium (Ca) and Strontium (Sr) example:

  • Both are in the same group (2A), which means they have the same number of valence electrons.

  • How many valence electrons do they have? Answer: two valence electrons each.

• Why this matters:

  • The identical valence electron count explains why Ca and Sr have similar chemical behaviors and properties in many contexts.

Quick Practice: Reading the Periodic Table for Valence Electrons

• For the main group elements, you can determine valence electrons by looking at the group number (Roman numeral designation or the A/IA–VIII groups):

  • Group 1A elements have 1 valence electron.

  • Group 2A elements have 2 valence electrons.

  • Carbon (Group 4) has 4 valence electrons.

  • Oxygen (Group 6) has 6 valence electrons.

• Practice takeaway:

  • To estimate an element’s bonding behavior, look at how many valence electrons it has in its outermost shell.

Conceptual Connections and Real-World Relevance

• Why the nucleus matters:

  • The nucleus provides mass and identity (Z determines the element).

  • Neutron count (N) influences isotopic stability and mass, with some isotopes being unstable or radioactive (e.g., Tritium). N does not affect chemical behavior directly, but it affects stability and nuclear properties.

• Why electrons and valence matter:

  • Chemical properties and bonding are driven largely by valence electrons, especially for main-group elements.

  • The periodic table’s arrangement reflects patterns in valence electron configurations, which drive bonding, reactivity, and material properties.

• Practical implications:

  • Isotopes have applications in medicine (e.g., Tc-99m in diagnostic imaging) and industry; understanding Z, A, and N allows you to determine nuclear composition and potential uses or risks.

  • The concept of molecular weight is essential in calculating dosages, reaction stoichiometry, and molecular interactions in biochemistry and pharmacology.

Summary of Key Formulas and Notation

• Mass number and neutron count:

  • $A = Z + N.$

  • $N = A - Z.$

• Neutral atom electron count:

  • $E = Z.$

• Isotope notation:

  • $^{A}_{Z}X$ where X is the element symbol, Z is the atomic number, and A is the mass number.

• Common isotopes of hydrogen (examples):

  • Protium: $^{1}_{1}H$ (N=0).

  • Deuterium: $^{2}_{1}H$ (N=1).

  • Tritium: $^{3}_{1}H$ (N=2).

• Atomic weight and molecular weight concepts:

  • Atomic weight (weighted average): $ext{Atomic weight} = \sum<em>i f</em>i A_i.$

  • Molecular weight (for a molecule): $M = \sum<em>i n</em>i M_i,$ e.g.,

  • $M(\mathrm{H_2O}) = 2\times M(\mathrm{H}) + M(\mathrm{O}) = 18\ \text{amu}.$

  • $M(\mathrm{C<em>6H</em>{12}O_6}) = 6\times 12 + 12\times 1 + 6\times 16 = 180\ \text{amu}.$

• Electron shell and subshell capacities (as described):

  • $s\text{-subshell capacity} = 2$ electrons.

  • $p\text{-subshell capacity} = 6$ electrons.

  • $d\text{-subshell capacity} = 10$ electrons.

  • $f\text{-subshell capacity} = 14$ electrons.

• Shell capacity buildup (as described):

  • 1st shell: 2 electrons (1s).

  • 2nd shell: 2 (s) + 6 (p) = 8 electrons.

  • 3rd shell: 2 (s) + 6 (p) + 10 (d) = 18 electrons.

  • 4th shell: +14 (f) = 32 electrons (in the simplified accounting).