Orbitals, Atomic Energy Levels, & Sublevels Explained - Basic Introduction to Quantum Numbers

Overview of Orbitals and Quantum Numbers

The video discusses orbitals, energy levels, sub-levels, and quantum numbers in detail.

Orbitals

• Definition: Orbitals are defined as regions in an atom where there is a high probability of finding an electron. They are not fixed paths but rather fuzzy clouds surrounding the nucleus, shaped by quantum mechanics.

• Visual Representation: Based on the Bohr model, which depicts electrons in orbits around the nucleus, orbitals are often illustrated to represent different shapes and configurations.

Energy Levels

• Principal Quantum Number (n):

  • Represents the main energy level of an electron in an atom.

  • Values: n = 1 (first energy level), n = 2 (second energy level), n = 3 (third energy level), and so on.

  • Electrons at higher energy levels (e.g., n=3) have more energy compared to those at lower levels (e.g., n=2). Each level can hold a maximum number of electrons given by the formula 2n².

Quantum Numbers

1. Principal Quantum Number (n):

   • Determines the size and energy of the orbital.

   • As n increases, the average distance of the electron from the nucleus increases and hence the energy of the electron also increases.

   • Electrons closer to the nucleus exist at lower energy levels, creating a gradient of energy levels.

2. Angular Momentum Quantum Number (l):

   • Describes the shape of the orbital, where shapes correspond to:

     • l = 0: s orbital (spherical shape)

     • l = 1: p orbital (dumbbell-shaped)

     • l = 2: d orbital (cloverleaf shape)

     • l = 3: f orbital (complex and varied shapes)

   • Relationship: l is constrained such that it is always less than or equal to n - 1, providing a limit to the shapes based on energy levels.

3. Magnetic Quantum Number (m_l):

   • Defines the orientation of the orbital in space.

   • For the s sublevel (where l = 0): there is only 1 possible orientation (m_l = 0).

   • For the p sublevel (l = 1): there are 3 orbitals with m_l values of -1, 0, +1 corresponding to the three possible orientations of p_x, p_y, and p_z.

   • For the d sublevel (l = 2): there are 5 orbitals, and m_l varies from -2 to +2, indicating five different orientations in 3D space.

4. Electron Spin (m_s):

   • Electrons rotate in an intrinsic manner characterized by the spin quantum number that can take on one of two values:

     • m_s = +1/2: Represents spin up (usually depicted as an up arrow).

     • m_s = -1/2: Represents spin down (depicted as a down arrow).

   • Each electron in an atom comprises a unique set of four quantum numbers (n, l, m_l, m_s), adhering to the Pauli exclusion principle which states no two electrons can have the same set of quantum numbers.

Examples of Quantum Number Calculation

• For a 2p⁵ electron:

  • n = 2 (indicating the second energy level)

  • l = 1 (identifying the p sublevel)

  • m_l = 0 (indicating the 5th electron in the p sublevel)

  • m_s = -1/2 (indicating the electron has spin down).

• For a 3d⁵ electron:

  • n = 3 (third energy level)

  • l = 2 (d sublevel)

  • m_l = +2 (indicating it’s in the fifth electron of the d sublevel)

  • m_s = +1/2 (indicating the electron has spin up).

Additional Resources

For further examples and a broader range of topics, refer to additional videos on quantum numbers, understanding the maximum number of electrons, and various chemistry topics available on platforms such as YouTube.