Chapter 3: Quantum Theory and the Electronic Structure of Atoms

3.1 Energy and Energy Changes

• Energy is the capacity to do work or transfer heat.
• All forms of energy are either kinetic or potential.
• Kinetic Energy: Energy of motion. Represented as: KE = (1/2)mu^2 where:
  • m is the mass of the object.
  • u is its velocity.
  • Thermal energy is a form of kinetic energy associated with the random motion of atoms and molecules.
• Potential Energy: Energy possessed by an object by virtue of its position.
  • Chemical energy is stored within the structural units of chemical substances.
  • Electrostatic energy is the potential energy resulting from the interaction of charged particles and is proportional to \frac{q1q2}{d}, where q1 and q2 represent two charges separated by a distance, d.
• Kinetic and potential energy are interconvertible.
• Law of Conservation of Energy: Energy can neither be created nor destroyed; when energy of one form disappears, the same amount of energy reappears in another form or forms.
• The SI unit of energy is the joule (J).
  • Defined as the energy possessed by a 2-kg mass moving at a speed of 1 m/s.
  • Also defined as the energy exerted when a force of 1 newton (N) is applied over a distance of 1 m.
  • Kilojoule (kJ) is used for large amounts of energy.

Worked Example 3.1

• Calculation of kinetic energy of a helium atom moving at 125 m/s using KE = (1/2)mu^2.
• The mass of the helium atom (4.003 amu) must be converted to kilograms to ensure units cancel properly, giving KE in joules.

Worked Example 3.2

• Comparison of attraction between charges using \frac{q1q2}{d} to compare the magnitudes of the two values.
• Doubling both charges causes a four-fold increase in the magnitude of electrostatic energy between charged particles.

3.2 The Nature of Light

• Visible light is a small component of the electromagnetic spectrum.
• The speed of light (c) through a vacuum is a constant: c = 2.998 \times 10^8 m/s.
• Relationship between speed of light, frequency, and wavelength: c = \lambda \nu, where:
  • \lambda is the wavelength in meters.
  • \nu is the frequency in reciprocal seconds (s⁻¹), also known as hertz (Hz).
• All forms of electromagnetic radiation travel in waves characterized by:
  • Wavelength (\lambda): Distance between identical points on successive waves.
  • Frequency (\nu): Number of waves passing through a point in 1 second.
  • Amplitude: Vertical distance from the midline of a wave to the peak or trough.
• Electromagnetic waves have both electric and magnetic field components with the same frequency and wavelength.
• The Double-Slit Experiment: Light passing through two closely spaced slits produces an interference pattern.
  • Constructive interference: Adding waves in phase.
  • Destructive interference: Adding waves out of phase.
  • Demonstrates the wave nature of light.

Worked Example 3.3

• Calculation of the frequency of a Nd:YAG laser with a wavelength of 532 nm using c = \lambda \nu.

3.3 Quantum Theory

• Classical physics, which describes macroscopic objects, is inadequate for subatomic particles.
• Quantization of Energy: Radiant energy is emitted or absorbed in discrete quantities (quanta).
• Max Planck suggested radiant energy is emitted or absorbed in discrete quantities.
• A quantum of energy is the smallest quantity of energy that can be emitted or absorbed.
• The energy E of a single quantum of energy is E = h\nu, where:
  • h is Planck's constant: h = 6.626 \times 10^{-34} J \cdot s.
• Energy is quantized rather than continuous.
• Albert Einstein used Planck's theory to explain the photoelectric effect.
  • Electrons are ejected from a metal surface exposed to light of a certain minimum (threshold) frequency.
  • The number of electrons ejected is proportional to the light's intensity (brightness).
  • Below the threshold frequency, no electrons are ejected, regardless of light intensity.
• Photons: