Definition Of Degenerate - Chemistry Dictionary - Chemicool

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Degenerate is used in quantum mechanics to mean 'of equal energy.' It usually refers to electron energy levels or sublevels.

degenerate-subshells

For example, orbitals in the 2p sublevel are degenerate - in other words the 2px, 2py, and 2pz orbitals are equal in energy, as shown in the diagram.

Likewise, at a higher energy than 2p, the 3px, 3py, and 3pz orbitals are degenerate.

And, at a still higher energy, the 3dxy, 3dxz, 3dyz, 3dx2 - y2, and 3dz2 are degenerate.

The number of different states of equal energy is called the degree of degeneracy or just degeneracy.

The degeneracy of p orbitals is 3; the degeneracy of d orbitals is 5; the degeneracy of f orbitals is 7.

We can also compare electron energies. In the following diagrams of hydrogen atom energy levels, the electrons are degenerate.

hydrogen-electron-ground-state hydrogen-electron-excited-state

One of the electrons is spin-up and the other is spin-down. In a non-uniform magnetic field, different spins respond differently; electrons with different spin orientations would no longer be degenerate - they would have slightly different amounts of energy. This is how electron spin was first detected in 1922 by the Stern-Gerlach experiment.

Notice also in these two diagrams that the 2s and 2p sublevels are degenerate. This is the case for hydrogenic atoms and ions - i.e. those with only one electron.

More Quantum Definitions

  • Aufbau Principle
  • Aufbau Principle Transition
  • Degenerate
  • Electron Spin
  • Electrons
  • Ground State
  • Heisenberg Uncertainty Principle
  • Hund's Rule
  • Hybridization
  • Hydrogenic
  • Light Absorption
  • Madelung Rule
  • Morse Potential
  • Orbital Approximation
  • Orbital Nodes
  • Orbitals
  • Pauli Exclusion Principle
  • Phonons
  • Quantum Numbers
  • Schrödinger Equation
  • Sublevel
  • Variation Theorem
  • Wave Function
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