Lecture Notes on Quantum Mechanics - Chapter 7

Key Concepts

• Quantum Mechanics: Understanding the behavior of electrons at a fundamental level.
• Heisenberg Uncertainty Principle: You cannot know both the position and momentum of an electron simultaneously.
• Schrodinger Equation: Calculates the probability of finding an electron in a region of space, forming what are known as orbitals.

Orbital and Probability

• Orbital: A region of space with a high probability of finding an electron.
• Hydrogen Example: Maximum probability of finding an electron is 57 picometers from the nucleus.

Quantum Numbers

Quantum numbers provide an "address" for the location of electrons within an atom. There are four quantum numbers:

1. Principal Quantum Number (n):

   • Values: 1, 2, 3, 4, ... up to infinity.
   • Describes orbital size and energy.
   • As 'n' increases, orbital size and energy increase.
   • Correlates with the Bohr model's shell concept.

2. Angular Momentum Quantum Number (l):

   • Values: 0 to n-1.
   • Determines the shape of the orbital.
   • Number and letter designations:
     • l = 0: s orbital (spherical shape)
     • l = 1: p orbital (dumbbell shape)
     • l = 2: d orbital (cloverleaf shape)
     • l = 3: f orbital (complex shapes)

3. Magnetic Quantum Number (m_l):

   • Values: From -l to +l.
   • Determines the number of orbitals of a given shape and their orientation in space.

4. Spin Quantum Number (m_s):

   • Describes the spin of electrons within an orbital.

Orbital Configurations

• First Shell (n=1):
  • Only 1s orbital.
• Second Shell (n=2):
  • 2s orbital plus three 2p orbitals (2px, 2py, 2pz).
• Third Shell (n=3):
  • 3s, 3p (three orbitals), 3d (five orbitals).
• Fourth Shell (n=4):
  • 4s, 4p (three orbitals), 4d (five orbitals), 4f (seven orbitals).

Electron Capacity

• First Shell: 2 electrons
• Second Shell: 8 electrons
• Third Shell: 18 electrons
• Fourth Shell: 32 electrons

Periodic Table Context

• Group 1 Elements: Have one electron in outer shell.
• Halogens (Group 7): Have seven electrons in outer shell.
• Elements in the same group show similar chemical properties due to similar outer shell electron configurations.

Conclusion

• Quantum mechanics provides a detailed understanding of electron configurations and their implications on chemical properties.
• Understanding orbital shapes and electron configurations is essential for grasping chemical behavior and element interactions.

This concludes the lecture on Chapter 7, focusing on the quantum mechanical model of the atom.