Orbital Theory and Quantum Numbers

Introduction

• Topics: Orbitals, Energy Levels, Sub-levels, Quantum Numbers
• Definition: An orbital is the most probable location to find an electron.

Bohr Model of the Atom

• Circular orbits representing energy levels
• Energy Levels:
  • First Energy Level: n = 1
  • Second Energy Level: n = 2
  • Third Energy Level: n = 3
• Electrons further from the nucleus have higher energy.

Principal Quantum Number (n)

• Describes: Size and energy of the orbital
• As n increases, distance from the nucleus increases
• Lower n (closer to nucleus) = Lower energy levels

Angular Momentum Quantum Number (l)

• Describes: Shape of the orbital
• Values of l:
  • l = 0: s orbital (sphere)
  • l = 1: p orbital (dumbbell)
  • l = 2: d orbital (clover shape)
  • l = 3: f orbital (complex)
• Shape and sublevel (e.g., s, p, d, f)
• Relationship with n:
  • l <= n - 1
  • n = 1: l = 0 (s)
  • n = 2: l = 0 (s), 1 (p)
  • n = 3: l = 0 (s), 1 (p), 2 (d)

Magnetic Quantum Number (m_l)

• Describes: Orientation of the orbital
• m_l Varies between -l and l
• Examples:
  • s orbital: l = 0, m_l = 0
  • p orbital: l = 1, m_l = -1, 0, 1 (px, py, pz)
  • d orbital: l = 2, m_l = -2, -1, 0, 1, 2
• Orbital Diagram (e.g., 3 orbitals for p, 5 orbitals for d)

Electron Spin Quantum Number (m_s)

• Describes: Electron spin direction
• Values: +1/2 (up) or -1/2 (down)
• Pauli Exclusion Principle: Every electron has a unique set of four quantum numbers.

Example Calculation

For Electron 2p^5

• n = 2 (second energy level)
• l = 1 (p sublevel)
• m_l = 0 (5th electron in p sublevel)
• m_s = -1/2 (spin down)

For Electron 3d^5

• n = 3 (third energy level)
• l = 2 (d sublevel)
• m_l = 2 (5th electron in d sublevel)
• m_s = +1/2 (spin up)

Additional Resources

• Check more videos on quantum numbers, electron configurations, and electron calculations on the Chemistry video playlist on YouTube.