midterm exam practice

Test Information

• The first 10 questions are multiple choice and automatically graded. Enter answers on the scantron sheet; answers in the test booklet will not receive credit.

• On the scantron sheet, provide: (1) your name, (2) ID number, and (3) exam version.

• Short Answer: Write in the provided space; final answers should be included in the boxes provided. For partial credit, if something is incorrect, mark it out and keep what you believe is correct.

• General Rules (Integrity): Violations of rules 3–6 are treated as academic integrity policy violations; penalties include failure of the exam or more severe sanctions.

• Rule specifics:

  • A numerical answer to a calculation without supporting work will not receive full credit even if correct.

  • Illegible writing will not be interpreted; neater handwriting increases chances of maximum credit.

  • No cell phones or electronic devices except a calculator are allowed at any time.

  • Do not borrow or lend a calculator; this is considered cheating and may result in a 0.

  • Only use a pen, pencil, eraser, and calculator.

  • If you must leave the room, you must turn in your exam paper; it will not be returned. Exceptions require medical documentation or SAILS.

Practical Advice for the Midterm

• Get a good night’s sleep.

• Redo homework problems.

• Go through a practice exam without looking at the key first.

• Bring a calculator you’re comfortable with; calculators may be limited and issued on a first-come, first-served basis.

• Be prepared; study concepts from my review and Tim’s review.

• When coming to class on Friday, sit one seat apart from other students; show up on time.

Atoms and Subatomic Particles: The Nucleus

• Most of an atom is empty space. Protons (positively charged) and neutrons (electrically neutral) are densely packed in the nucleus.

• Typical atomic radius: $1\,\mathrm{pm} = 1\times 10^{-12}\ \mathrm{m}$; typical atomic radius ~ $100\ \mathrm{pm}$.

• Nuclear radius is ~$5\times 10^{-3}\ \mathrm{pm}$, which is about 1/20{,}000 of the atomic radius.

• The identity of an atom (the element) is defined by the number of protons, the atomic number $Z$.

• Atomic mass is largely due to protons and neutrons in the nucleus; electrons contribute negligibly to mass.

• The atomic number is often denoted by $Z$.

Mass Number and Nuclear Composition

• Mass number $A$ is the sum of protons and neutrons: $A = Z + N$ where $Z$ = number of protons and $N$ = number of neutrons.

The Subatomic Particles

• Protons: located in the nucleus; positive charge.

• Neutrons: located in the nucleus; about the same mass as a proton; charge is zero.

• Electrons: distributed around the nucleus; occupy orbitals; much less mass than protons/neutrons (≈ $9.10936\times 10^{-28}\ \mathrm{g}$).

• Electron mass is negligible in contribution to atomic mass.

• Electron charge: $-1.6022\times 10^{-19}\ \mathrm{C}$; proton charge: $+1.6022\times 10^{-19}\ \mathrm{C}$.

• In charge units, a proton has charge $+1$ and an electron $-1$; atoms are electrically neutral when number of electrons equals number of protons.

Clicker Question (Phosphorus)

• Question: What is the atomic number of Phosphorus? Options: A, B, C, D (with values 15, 30.97, 5, 15 31 46)

• Answer: B; the atomic number is the top entry on the periodic table for Phosphorus, which is $Z=15$.

Isotopes and Atomic Mass

• Isotopes: Atoms with the same number of protons (same $Z$) but different numbers of neutrons (different $N$).

• All atoms of a given element have the same atomic number $Z$, but may have different neutron numbers; mass varies due to neutron number.

• Isotopes have identical chemical properties (roughly) but different masses and natural abundances.

• Example: Lithium has a fixed $Z=3$; naturally occurring lithium consists of isotopes with differing neutron counts.

Average Atomic Mass (Isotopic Abundance Weighting)

• Copper example: two stable isotopes — $^{63}\mathrm{Cu}$ with abundance $69.170\%$ and $^{65}\mathrm{Cu}$ with abundance $30.830\%$.

• Isotopic masses: $^{63}\mathrm{Cu} = 62.929\ \mathrm{Da}$; $^{65}\mathrm{Cu} = 64.928\ \mathrm{Da}$.

• Convert abundances to decimals and compute weighted average:

  • Decimal abundances: $0.69170$ and $0.30830$.

  • Average atomic mass: $\bar{M} = (0.69170)(62.929\ \mathrm{Da}) + (0.30830)(64.928\ \mathrm{Da}) = 63.545\ \mathrm{Da}$

• The result is the average atomic mass listed on the periodic table (without the word “average”).

Nuclear Stability and Nuclear Reactions

• Unstable nuclei are high-energy and decay to become more stable, releasing energy.

• Beta decay: a neutron converts to a proton and emits a beta particle (an electron). Result: increases atomic number $Z$ by 1; mass number $A$ remains the same.

• Alpha decay: a nucleus emits an alpha particle (Helium-4 nucleus: $^4\mathrm{He}$), losing two protons and two neutrons; decreases $Z$ by 2 and $A$ by 4.

• Nuclear reactions involve changes in the chemical identity (the element) of the atom, which is fundamentally different from typical chemical reactions. Energy governs stability in both cases.

Beta Decay Product (Clicker Question)

• Beta decay increases proton count by 1 (Z → Z+1) while A stays the same; therefore the correct product is the isotope with a higher atomic number but same mass number (answer C in the provided set).

Converting Between Atoms, Moles, and Grams

• Core skill: convert between atoms, moles, and grams.

• This underpins stoichiometry and many calculations in general chemistry.

• Example practice: converting 0.2500 moles of iron to grams.

• Given: atomic mass of Fe ≈ $55.845\ \mathrm{g\,mol^{-1}}$.

• Calculation: $0.2500\ \mathrm{mol\ Fe}\times \frac{55.845\ \mathrm{g\ Fe}}{1\ \mathrm{mol\ Fe}} = 13.96\ \mathrm{g\ Fe}$.

Atom vs Ion

• Neutral atoms have equal numbers of protons and electrons; no net charge.

• Ions form when atoms gain or lose electrons.

• Cation: positively charged (loses electrons); more protons than electrons.

• Anion: negatively charged (gains electrons); more electrons than protons.

Energy: Kinetic and Potential Energy

• Two primary types: kinetic energy (motion) and potential energy (position).

• Total energy of an object: $E_{\text{total}} = K + U$.

• Kinetic energy: $E_k = \tfrac{1}{2} m v^2$, where $m$ is mass and $v$ is velocity.

• All matter stores energy; energy exchange governs changes in systems.

Types of Potential Energy in Chemistry

• Chemical energy: energy stored in chemical bonds and structures (ions, molecules, etc.).

• Electrostatic energy: energy from interactions between charged particles; opposite charges attract, like charges repel.

• This is a qualitative description of Coulomb’s law; electrostatic energy can be described quantitatively with Coulomb’s law.

Spectroscopy and Light

• Spectroscopy studies interaction between light and matter.

• Lamps filled with the element’s gas emit light when excited by an electric current; emission lines reveal energy differences in atoms.

• Light carries energy; atoms release excess energy as photons during relaxation.

• Electromagnetic radiation: light is an electromagnetic wave with oscillating electric and magnetic fields perpendicular to each other and traveling at the speed of light.

The Electromagnetic Spectrum

• Range of EM waves from radio to gamma rays.

• Visible light spans roughly $400-700\ \mathrm{nm}$.

• Wavelength units: a nanometer (nm) is $10^{-9}\ \mathrm{m}$; a human hair is about $70\ \mathrm{µm} = 7.0\times 10^{4}\ \mathrm{nm}$.

Energy of Visible Light (Planck–Einstein)

• Energy of a photon: $E = h\nu$ where $h = 6.626\times 10^{-34}\ \mathrm{J\,s}$ and $\nu = c/\lambda$.

• Combine: $E = \dfrac{hc}{\lambda}$.

• Example: Red light with $\lambda = 700\ \mathrm{nm} = 7.00\times 10^{-7}\ \mathrm{m}$.

• Calculation steps:

  • $E = \dfrac{(6.626\times 10^{-34}\ \mathrm{J\,s})(3.00\times 10^{8}\ \mathrm{m/s})}{7.00\times 10^{-7}\ \mathrm{m}} = 2.84\times 10^{-19}\ \mathrm{J}$

  • Convert to eV using $1\ \mathrm{eV} = 1.602\times 10^{-19}\ \mathrm{J}$:

  • $E = \dfrac{2.84\times 10^{-19}\ \mathrm{J}}{1.602\times 10^{-19}\ \mathrm{J/eV}} = 1.77\ \mathrm{eV}$

• Result for red light: ≈ $1.75\ \mathrm{eV}$ (rounded as given in notes).

Wave-Particle Duality (de Broglie)

• Louis de Broglie proposed wave-particle duality: matter can exhibit wave-like properties.

• For atoms and electrons, quantum mechanics is required to describe motion realistically.

• Particle wavelength formula: $\lambda = \dfrac{h}{mv}$ where $h$ is Planck’s constant, $m$ mass, and $v$ velocity.

Hydrogen Atom: Excitation and Emission

• Energy level gaps in a hydrogen atom are not equally spaced; gaps get smaller as quantum number $n$ increases.

• Depending on excited state vs ground state, emitted photon energy can vary significantly.

• If energy is sufficient to reach infinity, the electron is ionized.

Quantum Numbers and Atomic Orbitals

• Principal quantum number $n$ defines orbital size and energy level; also defines electron shell.

• Angular momentum quantum number $l$ (0 to $n-1$) defines orbital shape and identity (s, p, d, f).

  • s: $l=0$; p: $l=1$; d: $l=2$; f: $l=3$.

• Magnetic quantum number $m<em>l$ defines orbital orientation within a subshell; $m</em>l \in [-l, +l]$ in integer steps.

• Orbital examples: for $l=1$ (p orbitals), there are 3 orientations corresponding to $m_l = -1, 0, +1$.

• The total number of orbitals in a shell increases with $n$: the shell has $n^2$ orbitals in total.

  • Example: $n=1$: 1s (1 orbital).

  • $n=2$: 1s + 3p (4 orbitals).

  • $n=3$: 1s + 3p + 5d (9 orbitals).

Shapes and Characteristics of Atomic Orbitals

• s orbitals: spherically symmetric; electron density depends only on distance from nucleus; highest density near nucleus; electron density decreases with increasing radius.

• p orbitals: oriented along Cartesian axes; three orientations; contain angular node(s) between lobes; for n>2, orbitals increase in size with $n$; sign of wavefunction is often shown by color (positive/negative lobes).

• d orbitals: present for $l=2$ when n>2; five orbitals; two angular nodes; commonly described shapes:

  • Four with cloverleaf shapes: $d<em>{xy}, d</em>{xz}, d<em>{yz}, d</em>{x^2-y^2}$.

  • The fifth: $d_{z^2}$ with a donut around the axis.

Nodes in Atomic Orbitals

• Nodes are regions of zero probability of finding an electron.

• Angular nodes: associated with the angular momentum quantum number $l$; planar surfaces of zero electron density.

• Radial nodes: spherical surfaces with zero electron density; number given by $\text{radial nodes} = n - l - 1$.

• Examples:

  • For a 2p orbital: $n=2, l=1$; radial nodes $= 2 - 1 - 1 = 0$ (no radial nodes), angular nodes $= l = 1$.

  • For a 3p orbital: radial nodes $= 3 - 1 - 1 = 1$ (one radial node).

Pauli Exclusion Principle

• No two electrons can have the same set of four quantum numbers ($n, l, m<em>l, m</em>s$).

• Each atomic orbital can hold at most two electrons, with opposite spins: $m<em>s = +\tfrac{1}{2}$ and $m</em>s = -\tfrac{1}{2}$.

• The electronic configuration determines all chemical properties.

Aufbau Principle and Hund’s Rule

• Aufbau Principle (building up): electrons fill orbitals in order of increasing energy, with no more than two electrons per orbital.

• If more than one orbital is available in a subshell, electrons occupy separate orbitals with parallel spins before pairing (Hund’s Rule).

• Ground-state configuration is obtained by applying these rules; excited-state configurations are anything else.

Carbon Electron Configuration (Illustrative Note)

• Common compact notation shows paired electrons in some subshells; shorthand often used is 1s2 2s2 2p4 for carbon, but Hund’s and Aufbau guide the detailed distribution among degenerate orbitals (2p: singly occupy each 2p orbital before pairing).

Key Formulas and Concepts Summary

• Mass number: $A = Z + N$

• Atomic number: $Z$ (number of protons)

• Neutron number: $N = A - Z$

• Electron charge (elementary charge): $e = 1.602\times 10^{-19}\ \mathrm{C}$; proton charge $+e$; electron charge $-e$.

• Kinetic energy: $E_k = \tfrac{1}{2} m v^2$

• Planck-Einstein relation: $E = h\nu$; $\nu = \dfrac{c}{\lambda}$; combined: $E = \dfrac{hc}{\lambda}$

• Wavelength of a particle (de Broglie): $\lambda = \dfrac{h}{mv}$

• Speed of light: $c = 3.00\times 10^{8}\ \mathrm{m/s}$

• Visible spectrum range: $\lambda_{visible} \approx 400-700\ \mathrm{nm}$

• Electron mass: $m_e \approx 9.10936\times 10^{-28}\ \mathrm{g}$

• Electron energy in context of light: example calculation yields ~$1.75\ \mathrm{eV}$ for $\lambda = 700\ \mathrm{nm}$.

Connections to Foundational Principles and Real-World Relevance

• Understanding isotopes informs chemical dating, medical isotopes, and natural abundances used in materials science.

• Nuclear decay concepts underpin radiometric dating, nuclear medicine, and safety considerations.

• Electron configuration and quantum numbers explain periodic trends, chemical reactivity, and bonding patterns.

• Wave-particle duality and de Broglie’s relation connect macroscopic intuition with quantum behavior essential for understanding electronics and spectroscopy.

Practical Implications and Ethical Considerations

• Accurate documentation of calculations and transparent partial-credit strategies help fairness in grading.

• Safe handling of radioactive materials and adherence to lab rules and guidelines are crucial in practical chemistry work.

• Ethical use of knowledge includes avoiding academic integrity violations and understanding the consequences of misconduct.

Worked Examples and Quick References

• Weighted average atomic mass example (Cu): $\bar{M} = (0.69170)(62.929\ \mathrm{Da}) + (0.30830)(64.928\ \mathrm{Da}) = 63.545\ \mathrm{Da}$

• Beta decay color-outline: increases $Z$ by 1, keeps $A$ constant; applies to transmutations within isotopes.

• Hydrogen excitation: energy gaps between levels vary with $n$; higher levels have smaller gaps; ionization occurs if energy exceeds binding energy.

• Orbital counts per shell: for $n=1\Rightarrow 1s\; (1\text{ orbital}); n=2\Rightarrow 1s + 3p \; (4\text{ orbitals}); n=3\Rightarrow 1s + 3p + 5d \; (9\text{ orbitals}).</p></li><li><p>Nodes in ns orbitals: number of nodes =$n-1$; radial nodes$= n - l - 1$; angular nodes equal to$l$$.

End of notes