Chem 2/27

Introduction to Light and Electrons

• Understanding connections between light and electrons help reveal electron location in atoms.

• Example problem: Calculate energy of light with a frequency of 610 kHz using the formula:

  • Energy (E) = h × frequency (ν)

    • h (Planck's constant) = 6.626 × 10^-34 joules·seconds

Energy Calculation

• Frequency must be converted from kilohertz to hertz.

  • 610 kHz = 610 × 10^3 Hz

• Energy calculation:

  • E = (6.626 × 10^-34) × (610 × 10^3)

  • E ≈ 4.04 × 10^-28 joules

• Result corresponds to choice A in provided options.

Wavelength and Frequency Relationships

• Formulas for calculations using different relationships:

  • Wavelength (λ) = c/frequency

  • Frequency = c/wavelength

• Calculating energy from wavelength leading to understanding properties of light.

Light Spectrum and Prisms

• Example of light dispersion:

  • When broadband white light (natural light) passes through a prism, it refracts and separates into visible colors (spectrum).

  • Water droplets can act as prisms, creating rainbows after a rainstorm.

Atomic Emission Spectra

• Different atomic gases emit various colors of light when energy is applied (e.g., neon signs emit pink/orange colors).

• Atomic spectrum principle:

  • Gases absorb and emit light based on internal electron movements.

• Example spectra:

  • Hydrogen: emits distinct lines, despite having only one electron.

  • Elements like neon, mercury exhibit more complex lines due to multiple electrons.

Balmer Equation and Hydrogen Spectrum

• Balmer's contribution: Assigning wavelengths of hydrogen's emission spectrum.

• Emission results from electrons transitioning between energy levels when they are excited and then relax to ground state, releasing photons (light).

• Balmer's equation for calculating wavelengths:

  • Using quantum numbers (n) for different energy levels.

  • Notable observations: more lines in UV and IR beyond visible spectrum.

Bohr's Atomic Model

• Model highlights electrons in defined orbits around the nucleus corresponding to quantized energy states.

• Bohr described electron transitions leading to light emission.

• Key contributions:

  • Ground state, excited state concepts.

  • Energy quantization principles.

  • Allowed calculations for hydrogen and simple ions.

• Limitations found when discussing heavier elements with more electrons.

De Broglie's Wave Nature of Matter

• De Broglie proposed matter, such as electrons, exhibits wave-like properties.

• Introduced relationship between mass and velocity for calculating wavelength:

  • λ = h/(m × v)

• Comparison examples:

  • A golf ball moving reveals minimal wave behavior due to its mass.

  • Electrons exhibit prominent wave properties due to their small mass.

Quantum Mechanics and Electrons

• Wave functions describe the probability of an electron's location in an atom.

• Quantum numbers define electron positions:

  • Principal quantum number (n): Shell (size and energy level).

  • Azimuthal quantum number (l): Shape of orbital (s, p, d, f).

  • Magnetic quantum number (m_l): Orientation of the orbital.

Orbital Shapes and Quantum Numbers

• The different shapes and conditions for orbitals derived from quantum mechanics:

  • s orbitals: spherical.

  • p orbitals: dumbbell-shaped (three orientations).

  • d orbitals: complex shapes (five orbitals).

  • f orbitals: even more complex (seven orbitals).

• Basic rules:

  • Each subshell can hold multiple orbitals defined by 2l + 1.

Summary of Key Concepts

• Bohr Model Successes and Limitations:

  • Defined electron positions in simple atoms (H).

  • Breakdowns with heavier elements.

• De Broglie's Insights:

  • Introduced wave-like behavior for electrons, contributing to quantum mechanics.

• Quantum Number System:

  • Crucial for accurately describing electron configurations in atoms (addressing elements with multiple electrons).

Conclusion

• Quantum mechanics provides a comprehensive framework for understanding atomic structure, electron behavior, and the relationship to light properties.