Atomic Structure & Absorption Spectroscopy - Quick Notes

Overview and agenda

• Plan: lecture with slides, quick problem skim, pointers on extra topics, and a Q&A at end. Time constraints mean not every problem type can be covered.

• Resources: class notes, tutoring available via Alpha Chi Sigma (Tues–Thurs, in the Hufflepuff common room). Use Canvas to access instructor office hours and slides.

• Focus today: dimensional analysis review, atomic structure, absorption concepts, and a brief molar mass review; end with absorption spectroscopy prep lab discussion.

Quick recap: essential study tools

• Class notes: highlight red flags or confusing topics; use textbook or Google for quick checks.

• Practice sets: focus on prefixes, unit conversions, and dimensional analysis.

• Practice problems mentioned:

  • MQ problems (dimensional analysis, unit conversions)

  • Quiz-style practice from the latest homework

• Strategy: learn the relationships between quantities, not memorize every problem; practice with new twists.

Atomic structure: core concepts

• Atoms consist of a tiny nucleus and surrounding electron cloud.

• Size scale: atom ~ $10^{-10} ext{ m}$; nucleus ~ $10^{-15} ext{ m}$

  • Atom is about $10^5$ times larger than its nucleus (rough scale).

• Nucleus contains protons and neutrons; electrons orbit outside.

• Subatomic particles and typical masses:

  • Proton: charge $+1$, mass ~ $1 ext{ amu}$

  • Neutron: charge $0$, mass ~ $1 ext{ amu}$

  • Electron: charge $-1$, mass ~ $0 ext{ amu}$ (often treated as negligible at this level)

• Atomic mass unit (amu): mass unit used for atomic-scale masses; $1 ext{ amu} <br>eq 1 ext{ g/mol}$ but is a defined unit for mass per atom.

• Protons and neutrons collectively contribute most of the atom’s mass; electrons contribute negligible mass.

Key definitions: atomic number, mass number, ions, isotopes

• Atomic number (Z): number of protons in the nucleus. Defines the element (e.g., Cl has Z = 17).

• Mass number (A): total number of protons and neutrons in the nucleus, A = Z + N.

• Neutral atoms: number of electrons equals Z (electrons = protons).

• Ions: charged species formed by changing electron count, not proton count.

  • Anion: extra electrons, negative charge.

  • Cation: fewer electrons, positive charge.

• Isotopes: atoms of the same element (same Z) with different neutron numbers (A varies).

• Example links:

  • Chlorine: Z = 17; mass number A varies by isotope (e.g., 35, 37).

  • Deuterium vs. ordinary hydrogen: same element (H) but different neutron count and mass.

Periodic table notation and reading a problem

• Notation idea used in class: element symbol with a subscript (Z) and a superscript (A).

  • Subscript Z indicates number of protons (atomic number).

  • Superscript A indicates mass number (protons + neutrons).

• To find neutrons: N = A − Z.

• For a neutral atom, electrons = Z; for ions, adjust electron count accordingly.

• Periodic table weight: atomic mass is a weighted average of isotopes based on natural abundance; shown as a decimal. Use when relating to real-world masses.

Practice problem patterns (brief strategies)

• If given Z and A, find protons, neutrons, and electrons (for neutral species: electrons = Z).

• If given mass and density, solve for volume or thickness using:

  • $\rho = \frac{m}{V}$ and for a rectangular solid, $V = l w h$ or in a small block, $V = x y z$.

• Common pitfall: watch units; convert to compatible units before plugging into formulas.

• Isotope calculations: use weighted average formula for atomic mass:
  $\text{Atomic mass} \approx \sum<em>i (\text{abundance}</em>i) \cdot (\text{mass}_i).$

Sample density/volume problem approach (conceptual)

• Given: density, mass, and a rectangular piece with known length and width; goal is thickness.

• Steps: relate mass to volume via $\rho = m/V$, compute V = m/\rho, and then solve for thickness using V = length × width × thickness.

• Important: convert between mass units (e.g., kg to g) to use convenient volume units (cm^3 = mL).

• If mass and density mix units (kg vs g), perform a unit conversion so that volume ends up in cm^3 (which equals mL).

• Always check units cancel to yield a sensible final length in cm or mm.

Absorption spectroscopy: light, color, and Beer's law

• Visible light range: approx $400 \text{ nm}$ to $700 \text{ nm}$. Color perceived is related to which wavelengths are transmitted vs absorbed.

• Color wheel concept: if sample appears yellow, it absorbs light opposite on the color wheel (complementary color, e.g., violet).

• Key terms:

  • Wavelength $\lambda$: distance between successive peaks (measured in nm for visible light).

  • Frequency $\nu$: number of waves per unit time; relation $c = \lambda \nu$ where $c\approx 3\ times 10^8\,\text{m/s}$.

  • Amplitude/intensity: how bright the wave is, does not change wavelength.

• Transmission vs absorption:

  • Transmittance $T = \frac{I}{I<em>0}$ where $I</em>0$ is incident intensity and $I$ is transmitted intensity.

  • Absorbance $A = -\log_{10}T$; Beer's law relates absorbance to concentration and path length.

• Beer's Law:

  • $A = \varepsilon \; c \; \ell$

  • where $\varepsilon$ is molar extinction coefficient, $c$ is concentration, and $\ell$ is path length.

• Why absorbance matters: plotting A versus concentration yields a linear relationship, which is easier to analyze than transmittance vs concentration.

• Practical lab connection: use a white light source, a sample, a wavelength-dispersing element, and a detector to build an absorbance spectrum; the peak absorbances reveal which wavelengths are removed by the sample.

Color and absorption intuition (practical takeaway)

• If a sample looks yellow, it likely absorbs violet; if it looks blue, it absorbs orange, etc. Complementary colors clarify which wavelengths are absorbed.

• Absorbance spectra show peaks at wavelengths where the sample absorbs strongly; high absorbance -> less transmission at that color.

• Beer's law is linear with respect to concentration; post-lab analyses use slope and intercept to extract meaningful constants.

Quick example highlights (from today’s discourse)

• Isotope example intuition: isotopes have same Z but different A due to neutrons; mass shows decimal due to natural isotope abundances; mass spectrometry reveals isotope distribution.

• Simple gold problem (conceptual): given a per-atom mass in ng, find number of atoms per gram by converting grams to ng and dividing. Result is a large number of atoms per gram (on the order of 10^21 for typical elemental masses).

Lab prep and next steps

• Absorption spectroscopy lab prep (LabPal simulation): set a wavelength, observe which colors are absorbed, and relate to color wheel and complementary colors.

• Be prepared to extract epsilon, concentration, and path length information from spectra for Beer's law applications.

• Next class: begin the actual absorption experiments and quantitative analysis; review Beer's law in detail and practice with real data.