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CH 301 Unit 1, Exam 1 Review Notes

1. Electromagnetic Radiation (EMR) Ranking & Calculation

Skills and Knowledge Required:
- Ability to rank electromagnetic radiation based on energy (E) and frequency (ν) or wavelength (λ)
- General understanding of some wavelength values.
- Calculation of energy using provided equations and constants (calculators not allowed).
Key Calculation Steps:
1. Convert wavelengths into meters. Know metric conversions.
2. Perform simple scientific notation math.
3. Understand that numbers will correspond to simplifications that facilitate math.
4. Note example scenarios typical of the exam for easier calculations.
Wavelength Ranges:
- Visible Light: 300 to 500 nm
- UV (Ultraviolet): 300 to 10 nm
- IR (Infrared): 800 nm to 1 𝜇m
- X-rays: 0.01 to 10 nm
Key Equations:
- Energy: $E = h \nu$
- Frequency: $ \nu = \frac{c}{\lambda}$
- Combined Energy-Wavelength: $E = \frac{hc}{\lambda}$
Constants:
- Planck's Constant (h): $h = 6.6 \times 10^{-34} ext{ Js}$
- Speed of Light (c): $c = 3 \times 10^{8} \text{ m/s}$
Ranking EMR Waves:
- Be cautious about whether to order from “most to least” or “least to most”.
Practice Exam Problems:
1. Correct order of increasing energy includes options using different electromagnetic waves. The correct answer is:
- A: Microwaves, visible light, UV light, X-rays, gamma rays
1. Given photon wavelength question evaluates energy calculation:
- If a photon’s wavelength is 663 nm, calculate energy:
  - D: $3.00 \times 10^{-19} ext{ J}$

2. Interactions Between Light & Matter

General Knowledge:
- Recognize types of EMR: Radio waves, Microwaves, Infrared (IR), Visible light, Ultraviolet (UV), X-rays, and Gamma rays (γ-rays).
Wavelength Ranges by Type:
- Radio Waves: 1 m to 100+ m
- Microwaves: 100 𝜇m to 1 m
- Infrared: 800 nm to 100 𝜇m
- Visible: 400 nm to 800 nm
- Ultraviolet: 10 nm to 400 nm
- X-rays: 0.01 nm to 10 nm
- Gamma Rays: < 0.01 nm
Impacts of EMR on Matter:
- Radio: Responsible for AM & FM signals.
- Microwaves: Cause molecular rotation, used in food heating (e.g., water and fat molecules).
- Visible Light: Detected by human eyes, causes photosynthesis.
- UV: Causes skin burns and cell mutations, limit exposure.
- X-rays: Used in medical imaging (non-invasive).
- Gamma rays: Emitted from stars (cosmic rays), involved with nuclear decay.
Practice Exam Problems:
1. When a given molecule absorbs infrared radiation, it:
- A: Begins to vibrate.
1. Impact of radio-frequency radiation:
- B: It makes the molecule rotate.

3. Failures of Classical Mechanics (Photoelectric Effect)

Understanding the Photoelectric Effect:
- Classical mechanics posited that light of sufficient intensity would eject electrons regardless of photon energy, which is incorrect.
- Planck & Einstein's model: Light as particles (photons) leads to a revised understanding that electrons are ejected only if photons have sufficient energy.
- Key Equation:
- $E = h \nu$ where energy is frequency-dependent.
- Electrons can only be ejected if energy exceeds a threshold (Work Function $\phi$ ).
Important Terminology:
- Kinetic Energy (K.E.) is given as availabe energy after the work function is met:
- $E = \phi + K.E.$
Practice Exam Problem:
1. Evaluating statements regarding the photoelectric effect to determine true or false:
- Correct options involve understanding when electrons are emitted in relation to light intensity and energy.
- Answer: E: Statements I and III are true.

4. Wave-Particle Duality of Light and Matter

Conceptual Understanding:
- Light behaves as both wave and particle, with classical mechanics being insufficient for explaining certain phenomena (e.g., photoelectric effect, blackbody radiation).
- Light as particles (photons) is necessary to explain quantization of energy.
- Wave behavior demonstrated by phenomena like diffraction and interference.
Matter as Wave and Particle:
- Matter has particle properties according to classical physics, yet exhibits wave-like behavior (de Broglie hypothesis). Electrons produce diffraction patterns as evidence.
Practice Exam Problem:
1. Proof of wave concept for matter:
- A: Matter can exhibit wave-like properties (electron diffraction).

5. de Broglie Theory

Understanding de Broglie Wave Equation:
- The relationship $mv = p$ where m is the mass and v is velocity.
- Due to $h = 6.63 \times 10^{-34}$ (small value), macroscopic objects have negligible wavelengths.
- Small particles (e.g., electrons) have measurable wavelengths.
Approximate Wavelengths:
- Electrons: $10^{-9} ext{ m}$
- Protons: $10^{-12} ext{ m}$
- Small molecules: $10^{-12} ext{ m}$
- Example of large objects: 100 kg human moving at 1 m/s has a wavelength of approximately $10^{-36} ext{ m}$ .
Practice Exam Problem:
1. Identify which object has the smallest wavelength:
- D: Molecules.

6. Rydberg Equation Calculation

Understanding the Rydberg Equation:
- The equation $ \nu = R \left( \frac{1}{nl^2} - \frac{1}{nh^2} \right)$ relates frequency to energy level transitions in hydrogen.
- $R$ is the Rydberg constant and is equivalent to the ionization energy of hydrogen.
Identifying Energy Levels:
- Energy levels approach each other as they move away from the nucleus following $\frac{1}{n^2}$ function.
Practice Exam Problems:
1. Identify the transition that emits the highest energy photon:
  - D: From n=2 to n=1 emits the highest energy photon.
2. Recognize transitions relevant to the Balmer series:
  - B: n=4 to n=2 and n=3 to n=2.

7. Quantum Mechanics Application – H Atom

Quantum Theory:
- Developed by Schrodinger, explaining electron probabilities rather than exact locations.
- Rules defining quantum states (n, l, ml, ms).
Quantum Numbers:
- n: Energy level; shell size, n = 1, 2, 3…
- l: Shape of orbital (l = n - 1)
- ml: Orientation of shape
- ms: Spin of electrons ( $\frac{1}{2}$ or $-\frac{1}{2}$ )
Practice Exam Problem:
1. Which quantum number determines atomic orbital size?
  - Answer: D: n.

8. Quantum Numbers Boundary

Understanding Quantum Numbers:
- Rules for quantum numbers:
- n = 1, 2, 3, …
- l = 0, 1, 2, … n - 1
- ml = -l, 0, l
- ms = +1/2, -1/2
Determining Maximum Electrons:
- Max electrons calculation given quantum numbers (2 electrons per orbital).
Examples:
- Max electrons for n = 1: 2.
- For n = 2 and n = 3 p-orbitals: 12 electrons.
Practice Exam Problems:
1. Find the max number of electrons for given sets of quantum numbers.
2. Identify which quantum number set doesn’t satisfy wave equation.

9. Periodic Table Nomenclature

Importance of the Periodic Table:
- Enables calculations of molar mass and elemental characteristics.
- Helps determine numbers of electrons, protons, and neutrons.
Key Definitions:
- Familiarize with terminology: period, group, family, block, main group, transition elements, alkali metals, noble gases, etc.
Practice Exam Problem:
1. Interpret potassium classification and position in the periodic table:
- Example Answer: C: potassium is in the family of alkali metals, located in the s block, making it a reactive element.

10. Aufbau, Hund, Pauli Theories

Electron Configuration Rules:
- Aufbau's Rule: Electrons fill lower energy orbitals first.
- Hund's Rule: Electrons spread out across degenerate orbitals before pairing.
- Pauli Exclusion Principle: No two electrons can share the same set of quantum numbers in an orbital.
Practice Exam Problems:
1. Identify incorrect application of Aufbau’s rule:
  - Answer will depend on arrangement illustrations provided by the exam.

11. Answer Key

Answers To Practice Exam Problems
1. EMR Ranking and Calculation:
- A. 2: D (Energy = $3 \times 10^{-19}$ J)
1. Interactions Between Light and Matter:
- A, D
1. Failures of Classic Mechanisms (Photoelectric Effect):
- E (Statements I and III are true)
1. Wave-Particle Duality of Light and Matter:
- A
1. de Broglie Theory:
- D
1. Rydberg Equation Calculation:
- D, B
1. Quantum Mechanics Application—H Atom:
- D
1. Quantum Numbers Boundary:
- D, A
1. Periodic Table Nomenclature:
- C
1. Aufbau, Hund, and Pauli Theory:
- B