Quantum Mechanics 8a - Spin I

Welcome to Quantum Mechanics 8, Spin

This video explores the concept of spin in quantum mechanics and its significance in atomic behavior.

The Number Two in Atomic Behavior

• The number two plays a significant role in atomic behavior.

• Hydrogen orbitals per energy level, when multiplied by two, correspond to the periods of the periodic table.

• Michelson and Morley discovered the fine structure of the hydrogen spectrum, revealing a split in spectral lines.

• Precise observations of other atomic spectra also showed examples of this fine structure.

Energy Level Splitting

• The development of quantum theory revealed that energy levels in atoms are split.

• Schrödinger's solution predicts that orbital types for a given energy level have the same energy.

• However, precise measurements show that s orbitals have single energy values while p and d orbitals are split into closely spaced energy levels.

Angular Momentum and Energy Level Splitting

• S orbitals have zero orbital angular momentum, while other orbitals have non-zero angular momentum.

• Orbitals with angular momentum experience an energy level splitting, but s orbitals with no angular momentum do not.

Zeeman Effect and Anomalous Zeeman Effect

• An atom in a magnetic field can produce the Zeeman effect, where electron orbital energies change based on z components of angular momentum.

• The Zeeman effect results in an odd number of line splittings due to an odd number of possible components.

• In some cases, such as the anomalous Zeeman effect, there is a splitting into an even number of lines.

Stern-Gerlach Experiment

• The Stern-Gerlach experiment using silver atoms demonstrated a splitting into two spots when exposed to a non-uniform magnetic field.

• Similar experiments with hydrogen atoms also showed a similar splitting into two spots.

Electron Spinning and Two-Valuedness

• Wolfgang Pauli proposed that the experimental results from the Stern-Gerlach experiment indicate that electrons have a two-valuedness.

• George Uhlenbeck and Samuel Goudsmit proposed that this two-valuedness is due to electron spinning, which creates angular momentum and a magnetic dipole.

Conclusion

The concept of spin in quantum mechanics explains energy level splitting and the behavior of atoms in magnetic fields. Electron spinning plays a crucial role in understanding these phenomena.

This summary provides an overview of the main topics covered in the video. For a more detailed understanding, it is recommended to watch the full video.

New Section

This section discusses the concept of spin in quantum mechanics and its relationship to classical phenomena.

Spin and Two-Valuedness

• Spin in quantum mechanics is represented by a z component of minus h bar over 2 or plus h bar over 2, referred to as spin down and spin up.

• The spinning of a body in a quantum context can explain the two-valuedness observed in experiments.

• Pauli avoided referencing classical phenomena, although classical spinning of a particle cannot explain the angular momentum of an electron.

• Electron spin is not describable classically.

New Section

This section explores the limitations of classical models when describing electron spin.

Limitations of Classical Models

• If an electron travels around a circle with radius r equal to the size of an atom, setting its orbital angular momentum equal to h bar yields a physically plausible velocity.

• However, for a spherical electron with mass m spinning such that the velocity on its surface is v and requiring the angular momentum to be h bar, even the largest plausible radius results in a surface velocity that exceeds the speed of light.

• There is no classical model that can explain the angular momentum of an electron's spin.

New Section

This section emphasizes that electron spin cannot be described classically.

Intrinsic Nature of Electron Spin

• The term "two-valuedness not describable classically" is abstract but can be simplified as "spin."

• Quantum mechanics approaches classical mechanics as quantum numbers increase, but this correspondence does not apply to spin.

• The spin quantum number s remains fixed at � and cannot be changed like orbital angular momentum.

• Spin is an intrinsic property of the particle, and its transition into a classical phenomenon cannot be observed.

New Section

This section discusses the use of the term "spin" despite its lack of correspondence to classical phenomena.

Use of the Term "Spin"

• The term "spin" is commonly used to describe electron spin, even though it does not correspond to any classical phenomenon.

• Previously discussed Bohr's correspondence principle, where quantum mechanics approaches classical mechanics for larger quantum numbers.

• Spin quantum number s remains fixed at �, which is peculiar compared to orbital angular momentum.

New Section

This section highlights the unique nature of electron spin and its inability to transition into a classical phenomenon.

Inability to Observe Quantum Mechanical Spin Transition

• Orbital angular momentum can change in both classical and quantum cases, but spin angular momentum cannot be changed.

• Spin is an intrinsic property of the particle, similar to mass and electric charge.

• Quantum mechanical spin does not transition into a corresponding classical phenomenon.

• The word "spin" is still used as it provides some understanding, even though it lacks a direct classical counterpart.