ch 2 intro ch 3

Introduction to Planck's Constant and Wavelength

• Planck's constant value: 6.626 x 10^-34 (units: Js)

• Used to solve for frequency in quantum mechanics.

• Example calculation: wavelength = 1.216 x 10^-7 m.

• Process of converting wavelengths: multiply by 10^9 to adjust units.

• Importance of understanding these calculations for exams.

Problem-Solving Approach

• Key steps to remember during problem-solving:

  • Identify what you're looking for (e.g., wavelength).

  • Determine the relevant equations or principles that guide you to the solution.

Introduction to Quantum Numbers

• Quantum numbers are used to describe the position and energy of electrons in an atom.

• Four Quantum Numbers for each electron in an atom:

  • Principal quantum number (n): Represents the distance from the nucleus.

  • Angular momentum quantum number (l): Represents the sub-energy level and shape of the orbital.

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

  • Spin quantum number (m_s): Represents the spin direction of the electron.

Understanding Quantum Numbers

Principal Quantum Number (n)

• Indicates the main energy level of an electron.

• Values: n = 1, 2, 3, etc.

• Higher values indicate electrons further from the nucleus.

Angular Momentum Quantum Number (l)

• Indicates the shape of the orbital:

  • s orbital (l = 0): spherical shape, can hold 2 electrons.

  • p orbital (l = 1): dumbbell shape, can hold 6 electrons.

  • d orbital (l = 2): clover shape, can hold 10 electrons.

  • f orbital (l = 3): complex shape, can hold 14 electrons.

Magnetic Quantum Number (m_l)

• Indicates the orientation of the orbital within a sublevel.

• For s orbital (l = 0): 1 orientation.

• For p orbital (l = 1): 3 orientations.

• For d orbital (l = 2): 5 orientations.

• For f orbital (l = 3): 7 orientations.

Spin Quantum Number (m_s)

• Indicates the spin direction of an electron in an orbital.

• Can be +1/2 (up) or -1/2 (down).

Assigning Quantum Numbers

• The process begins with n = 1 and increases upward:

  • For n = 1:

    • l = 0 → s orbital (only 2 electrons total).

  • For n = 2:

    • l = 0 (s) and l = 1 (p), can hold 8 electrons total (2 in s, 6 in p).

  • For higher n values: continue assigning based on available sublevels (l).

Application in Electron Configuration

• Understanding how to write electron configurations based on quantum numbers for elements like hydrogen and helium:

  • Hydrogen: 1s^1, with one electron in the first energy level.

  • Helium: 1s^2, with two electrons fulfilling the first orbital.

• Highlight the importance of knowing maximum electron capacities and configurations.

Key Principles for Filling Electron Orbitals

• Hund's Rule: Electrons go into separate orbitals before pairing.

• Fill orbitals from the lowest energy to the highest.

Example Questions for Study

1. How many orientations does a p orbital have?

2. Write out the box orbital diagram for 10 with quantum number assignment.

3. Explain the significance of no two electrons having the same set of quantum numbers.

Preparation for Examination

• Review topics on quantum numbers and their significance.

• Familiarize with diagrams and how to represent elements in electron configurations.

• Prepare ahead of the exam dates: significant dates include the seventh and eighteenth.

• Opportunity for extra credit and assistance during office hours.