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Chapter 7: Problem 96

Using only the periodic table inside the front cover of the text, write the expected ground-state electron configurations for a. the third element in Group 5 \(\mathrm{A}\) . b. element number \(116 .\) c. an element with three unpaired 5\(d\) electrons. d. the halogen with electrons in the 6\(p\) atomic orbitals.

Short Answer

Expert verified
The electron configurations for the specified criteria are: a. Antimony (Sb) with atomic number 51: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{3}\] b. Livermorium (Lv) with atomic number 116: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{6}7s^{2}5f^{14}\] c. Tantalum (Ta) with atomic number 73 and three unpaired 5d electrons: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{3}\] d. Astatine (At), a halogen with atomic number 85 and electrons in the 6p atomic orbitals: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{5}\]

Step by step solution

01

a. Third element in Group 5A

Locate Group 5A in the periodic table and find the third element in that group, which is Antimony (Sb). Antimony has an atomic number of 51, meaning it has 51 electrons in its ground state. The electron configuration for Antimony can be determined using the Aufbau principle, placing each electron in the lowest energy orbital available: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{3}\]
02

b. Element number 116

Element number 116 is Livermorium (Lv), which has 116 electrons in its ground state. The electron configuration for Livermorium is as follows: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{6}7s^{2}5f^{14}\]
03

c. An element with three unpaired 5d electrons

For this one, we assume all other subshells are fully occupied before filling up the 5d orbitals because it's the ground-state configuration. An element with three unpaired 5d electrons should have the following electron configuration: \[...4f^{14}5d^{3}\] This element is Tantalum (Ta), which has an atomic number of 73, and its complete electron configuration is: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{3}\]
04

d. The halogen with electrons in the 6p atomic orbitals

A halogen with electrons in the 6p atomic orbitals should have the following electron configuration pattern: \[...5d^{10}6p^{5}\] This element is Astatine (At), with an atomic number of 85. Its complete electron configuration is: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{5}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Periodic Table
The periodic table is a crucial tool in understanding elements and their electron configurations. It organizes elements based on their atomic number, electron configurations, and recurring chemical properties. Each element's position on the table helps predict its electron configuration, thus revealing its chemical behavior.
The table is divided into groups (vertical columns) and periods (horizontal rows). Groups often have elements with similar valence electron configurations leading to similar chemical properties.
For instance, Antimony (Sb), being the third element in Group 5A, has valence electrons in the p-block, specifically in the 5p orbitals. Understanding its placement helps deduce its electron configuration.
Aufbau Principle
The Aufbau principle is a guideline for determining the electron configurations of atoms in their ground states. It states that electrons fill atomic orbitals starting with the lowest energy levels before moving to higher levels.
  • The order followed is roughly 1s, 2s, 2p, 3s, 3p, 4s, and so on, progressing with increasing energy levels.
  • This "building up" of the electron orbitals leads us to the full electron configuration, as seen in Antimony: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{3}\]
Utilizing the Aufbau principle is key to predicting how electrons are distributed across an atom's orbitals.
Ground-State
An element's ground-state electron configuration is its most stable arrangement of electrons under normal conditions. It represents the lowest possible energy state for an atom.
Ground-state configurations are essential in indicating how an element will interact chemically. For example, Livermorium (Lv) with 116 electrons achieves stability with its ground-state configuration:
\[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{6}7s^{2}5f^{14}\]
Recognizing ground-state setups helps in forecasting reactivity and bonding behavior.
Unpaired Electrons
Unpaired electrons within an atom's configuration are electrons that do not have a partner in the same orbital. These play a significant role in determining the magnetic properties and reactivity of an element.
For example, Tantalum (Ta) has three unpaired 5d electrons in its ground-state configuration: \[...4f^{14}5d^{3}\]
  • Such unpaired electrons contribute to the magnetic characteristics of the element.
  • They also affect the way an element participates in chemical bonding.
The presence and number of unpaired electrons can predict how an element interacts with magnetic fields and other substances.

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