Showing Consistency with Hund's Rules

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SUMMARY

The discussion focuses on demonstrating that the ground states for sodium (Na), magnesium (Mg), and aluminum (Al) in the neon configuration (atomic numbers 11 to 18) adhere to Hund's rules. The configurations identified are [Ne]2S1/2 for Na, [Ne]1S0 for Mg, and [Ne]2P1/2 for Al. To verify consistency with Hund's rules, participants suggest calculating the energies of these configurations and comparing them against the established rules regarding multiplicity, angular momentum (L), and total angular momentum (J).

PREREQUISITES
  • Understanding of Hund's rules in quantum mechanics
  • Familiarity with atomic configurations and electron arrangements
  • Knowledge of energy calculations in quantum systems
  • Basic principles of atomic structure and spectroscopy
NEXT STEPS
  • Research methods for calculating atomic energy levels using quantum mechanics
  • Learn about the significance of multiplicity and angular momentum in atomic physics
  • Explore the application of Hund's rules in multi-electron atoms
  • Investigate the Bohr model and its relevance to energy calculations in atomic systems
USEFUL FOR

This discussion is beneficial for students of quantum mechanics, physicists studying atomic structure, and educators teaching advanced chemistry concepts related to electron configurations and energy states.

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Homework Statement


Show that the ground states for the first three elements in the “neon configuration” (Z=11 to 18) are consistent with Hunds rules.

Homework Equations


From Hyperphysics, the rules are:
1. The term with maximum multiplicity lies lowest in energy
2. For a given multiplicity, the term with the largest value of L lies lowest in in energy.
3. For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.

(in form 2s+1LJ)

3. The Attempt at a Solution
We know how to use Hund's rules to find the configuration. For the first three elements--Na, Mg, and Al--the configuration is [Ne]2S1/2, [Ne]1S0, and [Ne]2P1/2.

But how do we show consistency? Our best guess is that we find the energies of each element in their ground states and check it with the rules. How do we find energy though? Is it En? And if is, do we use the Bohr formula? Or something else?
 
Physics news on Phys.org
My attempted solution was right... I'll just leave this up in case anyone else wanted to know.
 

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