Why Do 1s and 2s Orbitals Have Different Electron Probabilities?

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Discussion Overview

The discussion centers on the differences in electron probability distributions for 1s and 2s orbitals, particularly focusing on the presence of nodes in their respective probability graphs. Participants explore the implications of these differences and seek clarification on the significance of nodes in atomic orbitals.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that the 1s orbital has no nodes while the 2s orbital does, questioning why this leads to different probabilities of finding an electron at various distances from the nucleus.
  • Another participant points out that while the 1s and 2s orbitals have similar structures, the presence of nodes in the 2s orbital affects the probability distribution.
  • A participant asks for clarification on the significance of nodes, suggesting that the 1s orbital appears as a cloud around the nucleus, implying a uniform probability of finding the electron within that cloud.
  • One participant introduces the concept of factoring the wavefunction into radial and angular components, indicating that while the angular parts of the 1s and 2s orbitals are the same, their radial parts differ.

Areas of Agreement / Disagreement

Participants express differing views on the implications of nodes and the nature of electron probability distributions, indicating that multiple competing perspectives remain without a consensus.

Contextual Notes

The discussion does not resolve the significance of nodes or the implications of the differences in radial functions for the 1s and 2s orbitals, leaving these aspects open to further exploration.

AdityaDev
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From the ψ2 vs r graph (i.e probability of finding an electron vs distance from nucleus graph), there are no nodes for 1s orbital while there is a node in the 2s orbital graph.But they have similar structures right? Then why is there a difference in finding the probability of finding an electron? Also, the p-orbitals 2p,3p,etc have similar structures. Then why is there a difference in number of nodes? Can someone explain this by providing images of 1s,2s orbitals?
 
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AdityaDev said:
Then why is there a difference in number of nodes?
What is the significance of the node? The image I have of 1s is a cloud enveloping the nucleus. Everywhere within this cloud has a chance of containing "the electron", hence no node.
 
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You can factorize the wavefunction into a radial function and the angular function (which is a spherical harmonic). For 1s and 2s, the angular part is the same, but the radial part isn't.
 

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