Ch.7 - Quantum MechanicsWorksheetSee all chapters
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Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Solution: Radial probability distributions for the 1s , 2s , and 3s orbitals of hydrogen. These plots show the probability of finding the electron as a function of distance from the nucle

Problem

The first graph is for 1s, and shows a sharp peak to about 90% of the Y-axis at around 0.5 angstroms (the most probable distance from the nucleus), before tapering to near-zero by 3 angstroms from the nucleus. The second graph is for 2s, which shows a low peak at around 0.5 angstroms then drops to 0 at 1 angstrom, which is a node.  Then the curve increases with a medium-width hump to a peak about 90% of the Y-axis at around 3 angstroms (the most probable distance from the nucleus), before tapering to near-zero by 8 angstroms. The third graph is for 3s, which shows a low peak at 0.5 angstroms, a node at 1 angstrom, a medium peak at around 2 angstroms, and another node at 4 angstroms.  After that, a very broad hump of maximum probability peaks around 7 angstroms (the most probable distance from the nucleus), before dropping to around 40% probability by 10 angstroms.


Radial probability distributions for the 1s , 2s , and 3s orbitals of hydrogen. These plots show the probability of finding the electron as a function of distance from the nucleus. As n increases, the most likely distance at which to find the electron (the highest peak) moves farther from the nucleus.

How many nodes would you expect in this function?