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Questions and Answers
What is the correct relationship for calculating the charge of an atom?
What is the correct relationship for calculating the charge of an atom?
From which particles is the mass of an atom primarily derived?
From which particles is the mass of an atom primarily derived?
What is indicated by the atomic number of an element?
What is indicated by the atomic number of an element?
Which unit is used to measure atomic mass?
Which unit is used to measure atomic mass?
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What calculation is performed to find the atomic mass of an element with multiple isotopes?
What calculation is performed to find the atomic mass of an element with multiple isotopes?
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For the isotope 24Mg, how many neutrons does it contain?
For the isotope 24Mg, how many neutrons does it contain?
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What is the charge of the ion 16O2-?
What is the charge of the ion 16O2-?
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How is the overall charge of an atom represented mathematically?
How is the overall charge of an atom represented mathematically?
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What does the De Broglie wavelength of a particle indicate?
What does the De Broglie wavelength of a particle indicate?
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Which statement best describes the Heisenberg Uncertainty Principle?
Which statement best describes the Heisenberg Uncertainty Principle?
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In the quantum mechanical model of the atom, what does a wave function represent?
In the quantum mechanical model of the atom, what does a wave function represent?
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What is the significance of quantum numbers in quantum mechanics?
What is the significance of quantum numbers in quantum mechanics?
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How does particle-wave duality impact our understanding of matter?
How does particle-wave duality impact our understanding of matter?
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What does the term 'quantum state' refer to?
What does the term 'quantum state' refer to?
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Which concept does the term 'wave function collapse' primarily relate to?
Which concept does the term 'wave function collapse' primarily relate to?
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What does the principle of superposition in quantum mechanics state?
What does the principle of superposition in quantum mechanics state?
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What does the equation $c = \lambda n$ represent in relation to electromagnetic radiation?
What does the equation $c = \lambda n$ represent in relation to electromagnetic radiation?
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How does the intensity of a wave relate to its amplitude?
How does the intensity of a wave relate to its amplitude?
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What is a significant limitation of Rutherford's model of the atom regarding electron behavior?
What is a significant limitation of Rutherford's model of the atom regarding electron behavior?
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According to quantum mechanics, what does the Heisenberg Uncertainty Principle state?
According to quantum mechanics, what does the Heisenberg Uncertainty Principle state?
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What is the main feature of the quantum mechanical model of the atom?
What is the main feature of the quantum mechanical model of the atom?
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In relation to the wave-particle duality, which of the following statements is true?
In relation to the wave-particle duality, which of the following statements is true?
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What is represented by quantum numbers in the quantum mechanical model?
What is represented by quantum numbers in the quantum mechanical model?
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What does the term 'De Broglie wavelength' refer to?
What does the term 'De Broglie wavelength' refer to?
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Study Notes
Course Information
- Course title: Atomic Structure
- Course code: (C 06J) CHEM 0901
- Instructor: Dr. Mark A. W. Lawrence
Course Schedule and Assessment
- 3 lectures per week
- Each section taught by a different person
- 1 lab session per week (15% of course grade)
- Lab attire, manual, and submission required
- Failing the lab = failing the course (FP)
- 1 tutorial per week (starting week 2)
- Tutorials contribute 5% to overall grade
- 2 course tests (each 5%)
- Final exam (70%)
- Options for final exam format include 2 x 2-hour written papers or 3 x 1-hour, 20-minute online papers
- Check course page for the schedule details.
- Topics include: Physical Chemistry, Atomic Structure, Gases, Thermochemistry, Inorganic Chemistry, and Organic Chemistry
Opening Remarks
- Physical Chemistry is the application of physics to chemistry
- Calculations are involved
- CSEC mathematics is sufficient
- Practice is essential for understanding concepts
- Reader should work through problems step-by-step to grasp concepts
- Units and their conversions (e.g., g, kg, cm, m) are important.
Atomic Structure: History
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Robert Boyle (1627-1691) established evidence for the atomic structure of matter; elements cannot be broken down further.
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Joseph Priestly (1733-1804) and Antoine Lavoisier (1743-1794) established the law of mass conservation (mass is neither created nor destroyed in chemical reactions.)
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Law of definite proportions (Joseph Proust 1754-1826): elements combine in specific, fixed proportions during chemical reactions, not random ones.
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John Dalton (1766-1844) proposed atomic theory & law of multiple proportions. Elements are made of tiny, indivisible particles called atoms. Atoms of the same element have the same mass. Different elements have different masses. Chemical combination of elements to form compounds occurs in small, whole-number ratios. Chemical reactions only rearrange atoms but don't change them.
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Dalton's law of multiple proportions is consistent with the idea that atom masses are fixed.
Atomic Structure: Experiments
- Thomson's Cathode Ray Tube Experiment: Discovered that atoms contained negatively charged particles (electrons) and deduced the charge-to-mass ratio of electrons. Suggested the plum-pudding model of the atom.
- Millikan's Oil Drop Experiment: Determined the charge and mass of an electron.
- Rutherford's Gold Foil Experiment: Discovered the atom's nucleus (dense, positively charged core) and showed that most of an atom's volume is empty space; atoms are mostly empty, with positive charge concentrated in a tiny central nucleus. Atoms have a very tiny, densely packed, positive charge center called the nucleus.
The Rutherford Atom
- Electrons are in the space around the nucleus.
- Electrons repel each other.
- Nucleus is a massive particle, identified as protons.
- Nucleus may also contain neutrons.
Atomic Structure: Experiments (Summary)
- Thomson's CRT experiment: Atoms contain negatively charged electrons; determined charge/mass ratio of electrons; proposed the plum pudding model.
- Millikan's oil drop experiment: Resolved the charge and mass of an electron.
- Rutherford's gold foil experiment: Provided evidence to verify existence of the nucleus; showed that atoms are mostly empty space.
Atomic Structure: sub-atomic Particles
- Data on electron, proton, and neutron mass and charge. Note proton mass is much greater than electron mass and neutron mass is slightly greater than proton mass
- The diameter of the nucleus (~10−15 m) is significantly smaller than the diameter of the atom (~10−10 m).
Lecture Summary
- Definition of an element via atoms.
- Atomic structure overview using subatomic particles.
- Relative positioning of subatomic particles.
- Charge and mass data of subatomic particles.
- Relative comparison of the diameter of the nucleus and the atom.
Atomic Number & Mass Number
- Nucleus is positive due to the presence of protons.
- Atomic number (Z): Number of protons in an atom's nucleus.
- Atom is neutral if the # of electrons = # of protons
- Elements differ by their number of protons in their nucleus. This atomic # (Z) is specific to each element.
- Mass number (A): Total number of nucleons (protons + neutrons) in an atom's nucleus.
- A = Z + N, where N is the number of neutrons.
Atomic Notation
- Mass number (A) and atomic number (Z) used to symbolize an element (e.g., 235U92)
Isotopes
- Isotopes are atoms of the same element with different numbers of neutrons but the same number of protons. This means the # of protons is constant in each isotope!
- Isotopes of an element have identical chemical properties; most have similar physical properties, except for properties that depend on mass.
- Most elements are mixtures of isotopes.
- Examples of isotopes: hydrogen-1 (protium), hydrogen-2 (deuterium), and hydrogen-3 (tritium).
Example Table
- Species | Atomic # | Proton # | Neutron # | Mass # | charge | # of electrons
- ----------- | ----------- | ----------- | ----------- | ----------- | ----------- | -----------
- 17O | 8 | 8 | 9 | 17 | 0 | 8
- 16O²⁻ | 8 | 8 | 8 | 16 | -2 | 10
- 24Mg | 12 | 12 | 12 | 24 | 0 | 12
- 24Mg²⁺ | 12 | 12 | 12 | 24 | +2 | 10
Isotopes - Continued
- Contrary to Dalton's theory, atoms of the same element do not always possess the same mass because of the presence of isotopes with varying # of neutrons.
- Atomic mass is the weighted average of the various isotopic masses.
Atomic Mass
- Atoms are extremely small.
- Atomic mass unit (amu) or dalton (Da) is used to measure atomic mass; 1 amu = 1/12 the mass of 12C atom = 1.660539 x 10⁻²⁴ g
- The mass number, used in atomic notation, is roughly equivalent to the isotopic mass of an atom in atomic mass units (amu) or daltons (Da)
Calculating Atomic Mass
- The relative atomic mass (average atomic mass) of an element is the sum of the fractional abundance of each isotope multiplied by the mass of that isotope.
The Line Spectrum
- White light consists of a continuous distribution of all possible visible wavelengths.
- A prism can separate white light into the different colors of the visible spectrum.
- Atoms, when excited (e.g., by heat or electricity), emit light at specific wavelengths or frequencies.
- This emitted light produces a line spectrum (a spectrum consisting of discrete lines or bands of color) rather than a continuous distribution of wavelengths (a continuous spectrum). Each atom produces a unique line spectrum.
Bohr’s Theory
- Atoms are stable even though classical physics implies that electrons should emit electromagnetic waves and spiral into the nucleus, which leads to an eventual collapse of the atom.
- Bohr's theory addresses the issue. Electron movement is restricted to specific orbitals with discrete energy levels. Atoms are stable because electrons only exist in these discrete quantized states, according to Bohr.
Bohr’s Postulates
- Electrons orbit the nucleus in specific, quantized orbits which are restricted to specific energy levels and therefore specific distances from the nucleus. This was in contrast to the notion that there is some range of allowed orbits within atoms.
- Electrons do not continuously emit electromagnetic radiation when in a stationary state (an orbit with a fixed energy).
- Electrons only emit or absorb energy by transitioning between discrete energy levels. The emitted energy is in the form of a photon.
Bohr Model Successes and Failures
- Bohr Model Successes:
Better depiction of atoms: electrons move in quantized/discrete orbits. Explains linespectra and ionization energy, especially in atoms with one electron.
Excellent agreement with experimental data
- Bohr Model Failures:
Unable to predict line spectra for more complex atoms. Unable to explain why the energy levels are quantized or why atoms make transitions. Unable to explain fine-structure of atomic emission lines. Unable to explain atomic bonding.
Wave-Particle Duality (de Broglie Relationship)
- Electromagnetic energy travels at the speed of light, c = 2.998 x 10⁸ m/s. The speed of the wave is related to the wavelength (λ) and frequency (v) by the equation: c=λv.
- Planck constant, h = 6.626 x 10⁻³⁴ J⋅s
- Electrons and other matter particles also exhibit wave-like properties or wave-particle duality, and its wavelength (λ) is related to its momentum (mv) by the de Broglie relationship: λ = h/mv.
Quantum Mechanics and the Heisenberg Uncertainty Principle
- Quantum mechanics is a theory that describes the physical properties of nature at the scale of atoms and subatomic particles.
- Quantum mechanics abandons the notion of electrons orbiting the nucleus in defined, fixed paths.
- The Heisenberg Uncertainty Principle states that it is impossible to know precisely both the position and momentum of a particle (such as an electron) at the same time with arbitrary accuracy. The more precisely that one property is known, the less precisely the other can be known. (x)(Δmv) > h/4π
Wave Functions and Quantum Numbers
- Schrödinger's equation describes atomic structure using wave functions and quantum numbers.
- Wave function (Ψ): Provides probability of locating an electron in a specific region of space within an atom, determined by four quantum numbers.
- Quantum numbers define the properties of electron orbits/states and provide detailed descriptions of the possible types of electron orbitals within an atom. There are four, important quantum numbers to note for an electron.
Quantum Numbers
- Principal quantum number (n): Defines the energy level and the average distance of the electron from the nucleus.
- Angular momentum quantum number (l): Defines the shape of the electron orbitals
- Magnetic quantum number (ml): Defines the orientation of the electron orbit in space; describes a particular electron orbital.
- Spin quantum number (ms): defines the spin quantum number of electrons within an atom; describes the spin orientation of electrons in the orbital.
Orbital Shapes
- Different shapes of electron orbitals (s, p, d, f). Illustrates what different orbitals look like in 3D space.
Energy Levels of Different Orbitals
- Energy levels of different orbitals. Illustrates how energy levels of individual orbitals vary for multi-electron hydrogen atoms.
Electronic Configurations of Multielectron Atoms
- Electronic configurations of multielectron atoms in the first few rows of the periodic table.
- Aufbau principle: Electrons fill the orbitals with the lowest energy first
- Hund's rule: Any two degenerate orbitals are filled with one electron with the same spin prior to filling it again with another electron (with the opposite spin).
Electronic Configurations of Multielectron Atoms: Transition Elements
- Electronic configurations of transition elements. Explains the order of filling electrons in transition elements.
Summary
- Summary of the material covered in the lectures.
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