Textbook Question
Why does the number of elements in successive periods of the periodic table increase by the progression 2, 8, 18, 32?
Ch.5 - Periodicity & Electronic Structure of Atoms
Chapter 5, Problem 101
Order the orbitals for a multielectron atom in each of the following lists according to increasing energy. (a) 4d, 3p, 2p, 5s (b) 2s, 4s, 3d, 4p (c) 6s, 5p, 3d, 4p
Verified step by step guidance1
Step 1: Understand the order of filling orbitals using the Aufbau principle, which states that electrons fill orbitals starting from the lowest energy level to the highest. The order is determined by the n+l rule, where n is the principal quantum number and l is the azimuthal quantum number.
Step 2: For each list, calculate the n+l value for each orbital. The orbital with the lowest n+l value is filled first. If two orbitals have the same n+l value, the one with the lower n value is filled first.
Step 3: For list (a) - Calculate n+l for each orbital: 4d (n=4, l=2, n+l=6), 3p (n=3, l=1, n+l=4), 2p (n=2, l=1, n+l=3), 5s (n=5, l=0, n+l=5). Order them by increasing n+l value.
Step 4: For list (b) - Calculate n+l for each orbital: 2s (n=2, l=0, n+l=2), 4s (n=4, l=0, n+l=4), 3d (n=3, l=2, n+l=5), 4p (n=4, l=1, n+l=5). Order them by increasing n+l value, considering n if n+l is the same.
Step 5: For list (c) - Calculate n+l for each orbital: 6s (n=6, l=0, n+l=6), 5p (n=5, l=1, n+l=6), 3d (n=3, l=2, n+l=5), 4p (n=4, l=1, n+l=5). Order them by increasing n+l value, considering n if n+l is the same.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Aufbau Principle
The Aufbau Principle states that electrons occupy the lowest energy orbitals first before filling higher energy levels. This principle is fundamental in determining the electron configuration of atoms, as it guides the order in which orbitals are filled based on their energy levels.
Recommended video:
Guided course
02:05
Uncertainty Principle Formula
Energy Levels and Sublevels
In multielectron atoms, energy levels are divided into sublevels (s, p, d, f) that have different energy states. The energy of these sublevels is influenced by both the principal quantum number (n) and the type of sublevel, with d and f sublevels generally being higher in energy than s and p sublevels at the same principal quantum number.
Recommended video:
Guided course
01:26Nature of Energy
Hund's Rule
Hund's Rule states that electrons will fill degenerate orbitals (orbitals of the same energy) singly before pairing up. This rule is important for understanding the distribution of electrons in orbitals and helps predict the stability and energy of electron configurations in multielectron atoms.
Recommended video:
Guided course
00:28Solubility Rules
Related Practice