Atomic Notation and Quantum Mechanics

Overview of Today's Topics

• Finish Chapter 1: Atomic Notation

• Start Chapter 2: Properties of Light and Energy

  • Key experiments leading to Quantum Mechanics

• Study Chapter 1 and skim Chapter 2 (Sections 2.1-2.3)

• Continue working on Homework C11_HW2:

  • Questions 1-7 relate to Chapter 1 topics

  • Questions 8-13 are from the beginning of Chapter 2 (Sections 2.1-2.3)

• Reminder: Weekly Homework/Quiz is always due Sunday at 11:59 PM

Atomic Notation

• Atomic symbols summarize subatomic composition, crucial in chemistry as it defines what an element is made of and its structure.

  • Elements are represented by a one or two-letter symbol.

  • Atomic Number (Z): The number of protons in an atom, indicating the specific element, written as a subscript before the symbol.

  • Example: in $_{6}^{12}C$, 6 is the atomic number (Z).

  • Mass Number: The total number of protons and neutrons in an atom's nucleus, written as a superscript before the symbol.

  • Example: in $_{6}^{12}C$, 12 is the mass number.

  • WebAssign notation: Use caret (^) for superscripts and underscore (_) for subscripts.

  • For ions, charges are indicated as right superscripts (e.g., $^{2+}$ or $^{-}$).

Isotopes

• Isotopes: Variants of an element that differ in neutron count while having the same number of protons.

  • Example: Lithium isotopes

  • Lithium-6: $_{3}^{6}Li$ has 3 neutrons

  • Lithium-7: $_{3}^{7}Li$ has 4 neutrons.

• The existence of isotopes challenges Dalton’s second postulate, which stated that all atoms of an element are identical in mass.

Periodic Table

• The Periodic Table summarizes information about atoms, elements, and trends in their chemical and physical properties.

  • Elements are arranged in increasing atomic number.

  • Key concept: The Average Atomic Mass reflects the weighted average of all isotopes.

Characteristics of Atoms and Ions

• Key characteristics include charge, mass, and size:

  • Charge: Defined by the difference in the number of protons and electrons.

  • Net charge formula: ext{Charge} = ext{# p} - ext{# e} .

  • An atom has a neutral charge, cations are positively charged, and anions are negatively charged.

  • Mass (in atomic mass units, amu) is nearly the sum of neutrons and protons.

  • Size is related to the number of electrons:

  • More electrons = larger size (all else constant).

  • More protons = smaller size due to increased positive attraction.

  • Compounds form due to electrostatic attractions (+/-) and sharing of electrons.

Historical Progression of Atomic Theory

• 1800s: Dalton proposed a model of atoms as building blocks of matter; established relationships between mass, volume of gases, and atomic counting.

• 1830s: Berzelius developed chemical notation for describing compositions and reactions.

• 1900: Key developments in atomic theory:

  • J.J. Thomson discovered the electron (first subatomic particle).

  • Becquerel and Rutherford revealed radioactivity involves atoms emitting subatomic particles, and elemental identity can change.

  • Rutherford proposed a nuclear model of the atom.

  • Millikan measured the electron's fundamental charge.

  • Soddy established isotopes; Chadwick characterized the neutron (1932).

• Chapter 2 anticipates a shift in thinking involving quantum theory (early 20th century).

Properties of Light

• Electromagnetic Radiation (Light): Produced by oscillating charges (e.g., moving electrons), exhibiting wave properties.

Wave Properties of Light

• Light can be mathematically defined using:

  • Amplitude: Height of the wave.

  • Wavelength (0): Distance between consecutive peaks.

  • Frequency (C6): Number of waves that pass a fixed point in a unit of time.

  • Speed of Light (c): Defined by the equation:
    c = 0 C6 = 3.00 imes 10^{8} ext{ m/s} .

• Example: For red light,

  • Frequency: $<br>u = 4.6 imes 10^{14} ext{ s}^{-1}$.

  • Wavelength: 0 = 650 ext{ nm} (where 1 nm = $10^{-9} ext{ m}$).

• Key idea: Unique wavelengths in the visible spectrum correlate to specific colors.

Observations in Light Behavior

Observation 1: Ultraviolet Catastrophe

• Ultraviolet Catastrophe: Classical physics failed to explain light emitted from very hot objects, predominately visible light but less ultraviolet light.

• Max Planck’s Resolution: Proposed that energies are quantized, with the energy of each quantum defined as: $riangle E = h u$

  • Where h is Planck's constant: $h = 6.626 imes 10^{-34} ext{ J.s}$ (1918 Nobel Prize in Physics).

• Light behaves as a wave, but has some particle-like properties.

Observation 2: Photoelectric Effect

• Metals emit electrons when light strikes them, but classical theory couldn't explain the dependence on light intensity:

  • No ejected electrons until a threshold frequency is reached, regardless of intensity.

  • The ejected electron's kinetic energy increases with the light frequency:
    $E<em>{ ext{photon}} - E</em>{ ext{threshold}} = E_{ ext{leftover}}$.

  • One photon ejects one electron, with energy proportional to light frequency:
    $E = h<br>u$.

Summary of the Photoelectric Effect

• Light can be modeled as photons (quanta) related to Planck's theories.

  • Photon energy: directly proportional to frequency $<br>u$, and inversely proportional to wavelength 0 :
    c = 0
    u

  • Memorization aids:

  • $E = h<br>u$

  • Derived relation: c = rac{h}{0} .

Atomic Emission Spectra

• Light enables the measurement of energy changes in electrons, exemplified by hydrogen as the simplest case.

Niels Bohr's Model of the Hydrogen Atom

• Bohr's Model: Expanded upon Planck's and Einstein's theories.

  1. Electrons can only occupy specific energy orbits.

  2. Electrons in these orbits have defined, quantized energies not emitted as radiation.

  3. Energy is emitted or absorbed only during transitions between orbits, represented as:
     $riangle E = h<br>u$.

  4. Successfully explained the hydrogen spectrum (1922 Nobel Prize in Physics).

  • Energy at specific levels:
    $E_n = -2.178 imes 10^{-18} ext{ J} rac{1}{n^2}$.

  • Energy transition:
    riangle En = -2.178 imes 10^{-18} ext{ J}igg( rac{1}{nf^2} - rac{1}{n_i^2} igg) = h
    u .

Photon Emission and Energy Levels

• Photons are created or destroyed when electrons transition between energy levels.

• Example:

  • If an electron transitions from the n=4 level to the n=2 level, the emitted light's color corresponds to the energy difference.

• Energy levels for hydrogen illustrated in diagrams; higher levels correspond to higher energy.

• The lowest energy state is called the ground state (n=1), while others are excited states.

• Key results and further homework: Use charts and equations related to Bohr's model to assist in understanding electron transitions and energy differences.