Consider the excited state transition 1s¹2p¹ → 1s¹3d¹ of a helium atom and answer the following related questions: (i) Find the number of microstates belonging to each of the confi... Consider the excited state transition 1s¹2p¹ → 1s¹3d¹ of a helium atom and answer the following related questions: (i) Find the number of microstates belonging to each of the configuration. (ii) Derive the energy terms arising from the two configurations. [Hint: Each of the configuration will give rise to 2 energy terms] (iii) Find the spin-orbit energy states associated with each of the energy terms.
Understand the Problem
The question is asking us to analyze the excited state transition of a helium atom by finding the microstates for each configuration, deriving energy terms from those configurations, and identifying the associated spin-orbit energy states. This involves applying concepts from quantum mechanics related to electron configurations and their associated energy levels.
Answer
For 1s¹2p¹: 12 microstates, terms are ^1P and ^3P; For 1s¹3d¹: 30 microstates, terms are ^1D and ^3D.
[{"configuration":"1s\u00b92p\u00b9","microstates":"12 (Using the formula (2L+1)(2S+1), for L = 1, S = 1/2)","term_symbols":["^1P","^3P"]},{"configuration":"1s\u00b93d\u00b9","microstates":"30 (Using the formula (2L+1)(2S+1), for L = 2, S = 1/2)","term_symbols":["^1D","^3D"]}]
Answer for screen readers
[{"configuration":"1s\u00b92p\u00b9","microstates":"12 (Using the formula (2L+1)(2S+1), for L = 1, S = 1/2)","term_symbols":["^1P","^3P"]},{"configuration":"1s\u00b93d\u00b9","microstates":"30 (Using the formula (2L+1)(2S+1), for L = 2, S = 1/2)","term_symbols":["^1D","^3D"]}]
More Information
The term symbols ^1P and ^3P indicate singlet and triplet states for p-orbitals, while ^1D and ^3D indicate singlet and triplet states for d-orbitals.
Tips
A common mistake is to miscount possible microstates by ignoring multiplicity and orbital contributions properly.
Sources
- 11.2.1: Finding Microstates and Term Symbols - Chemistry LibreTexts - chem.libretexts.org
- Solved A possible excited state for the helium atom has the - Chegg - chegg.com
- 8.8: Term Symbols Gives a Detailed Description of an Electron - Chemistry LibreTexts - chem.libretexts.org
