SPS 101 Principles Quiz on Orbital Energy

Energy Levels and Sublevels

• Sublevels increase in energy as follows: ns < np < nd < nf < ng.
• For principal quantum number n = 1: only the 1s sublevel exists; n = 2 includes 2s and 2p; n = 3 includes 3s, 3p, and 3d; n = 4 includes 4s, 4p, 4d, and 4f.

Magnetic Quantum Number (ml)

• Determines the orientation of atomic orbitals relative to the nucleus.
• Allowed values of ml vary from –l to +l.
• The number of ml values corresponds to the number of orbitals in a subshell, calculated using (2l + 1).
• Example for l = 1 (p subshell): three p orbitals with ml values of -1, 0, and +1.

Spin Quantum Number (ms)

• Describes the spin and magnetic behavior of electrons, indicating rotation along their own axis.
• Electrons can have two spin states: spin up (½) and spin down (-½).
• Only two electrons may occupy the same orbital, requiring opposite spins.

Electron Configuration

• Follows the exclusion principle for assigning electrons to orbitals.
• Example configurations:
  • Hydrogen (H): 1s¹
  • Helium (He): 1s²
  • Neon (Ne): 1s² 2s² 2p⁶.

Hund’s Rule

• States that degenerate orbitals are first filled with one electron each before pairing occurs.
• Fewer repulsive interactions occur when electrons are distributed in separate orbitals.

Bohr's Model of the Hydrogen Atom

• Allowed energy states of the H electron are expressed as: [ E_n = -R_H \left( \frac{1}{n^2} \right) ]
• Rydberg constant ( R_H = 2.18 \times 10^{-18} ) J.
• Transitions between energy levels involve absorption or emission of electromagnetic radiation, corresponding to spectral lines.

Quantum Theory of the Atom

• Developed through contributions from Louis de Broglie, Werner Heisenberg, and Erwin Schrödinger.
• Explains electron behavior in atoms and their role in chemical and physical properties.

de Broglie Relation

• Proposes that particles, like electrons, exhibit wave properties, connecting wave properties to kinetic energy.
• Wavelength (( \lambda )) associated with mass (m) and velocity (v): [ \lambda = \frac{h}{mv} ] where ( h = 6.626 \times 10^{-34} ) J.s.

Heisenberg Uncertainty Principle

• States that one cannot precisely know both the position and momentum of a particle simultaneously.
• Expressed mathematically as: [ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} ]

Schrödinger Equation

• Developed in 1926 to describe electron behavior and energy in atoms: [ H\psi = E\psi ]
• The wave function (( \psi )) represents a region of space with a high probability of finding an electron.
• The electron cloud diagram shows areas of varying electron density, indicating probabilities of electron location.

Quantum Numbers

• Four quantum numbers describe electrons:
  • Principal quantum number (n) indicates energy level.
  • Angular momentum quantum number (l) relates to subshell type.
  • Magnetic quantum number (ml) defines orbital orientation.
  • Spin quantum number (ms) specifies electron spin direction.

Test your understanding of the increasing energy levels of sublevels within a principal energy level in atomic structure. This quiz covers the organization of orbitals from ns to ng as well as the arrangement of n values and their corresponding l sublevels. Perfect for reinforcing concepts in quantum chemistry.