Problem 102
Question
Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) Br, (b) Ga, (c) Hf, (d) Sb, (e) Bi, (f) Sg.
Step-by-Step Solution
Verified Answer
The condensed electron configurations and numbers of unpaired electrons for the ground state of the given elements are as follows:
(a) Br: \(\mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^5}\), 1 unpaired electron
(b) Ga: \(\mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^1}\), 1 unpaired electron
(c) Hf: \(\mathrm{[Xe]\, 6s^2\, 4f^{14}\, 5d^2}\), 2 unpaired electrons
(d) Sb: \(\mathrm{[Kr]\, 5s^2\, 4d^{10}\, 5p^3}\), 3 unpaired electrons
(e) Bi: \(\mathrm{[Xe]\, 6s^2\, 4f^{14}\, 5d^{10}\, 6p^3}\), 3 unpaired electrons
(f) Sg: \(\mathrm{[Rn]\, 7s^2\, 5f^{14}\, 6d^4}\), 4 unpaired electrons
1Step 1: Find the location in the periodic table
Bromine is in the 4th period and the 17th group in the periodic table, so it has 35 electrons.
2Step 2: Write the condensed electron configuration
Bromine's condensed electron configuration is:
\[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^5} \]
3Step 3: Determine the number of unpaired electrons
In the 4p orbital, there is 1 unpaired electron.
(b) Ga (Gallium)
4Step 1: Find the location in the periodic table
Gallium is in the 4th period and the 13th group in the periodic table, so it has 31 electrons.
5Step 2: Write the condensed electron configuration
Gallium's condensed electron configuration is:
\[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^1} \]
6Step 3: Determine the number of unpaired electrons
In the 4p orbital, there is 1 unpaired electron.
(c) Hf (Hafnium)
7Step 1: Find the location in the periodic table
Hafnium is in the 6th period and the 4th group in the periodic table, so it has 72 electrons.
8Step 2: Write the condensed electron configuration
Hafnium's condensed electron configuration is:
\[ \mathrm{[Xe]\, 6s^2\, 4f^{14}\, 5d^2} \]
9Step 3: Determine the number of unpaired electrons
There are 2 unpaired electrons in the 5d orbital.
(d) Sb (Antimony)
10Step 1: Find the location in the periodic table
Antimony is in the 5th period and the 15th group in the periodic table, so it has 51 electrons.
11Step 2: Write the condensed electron configuration
Antimony's condensed electron configuration is:
\[ \mathrm{[Kr]\, 5s^2\, 4d^{10}\, 5p^3} \]
12Step 3: Determine the number of unpaired electrons
There are 3 unpaired electrons in the 5p orbital.
(e) Bi (Bismuth)
13Step 1: Find the location in the periodic table
Bismuth is in the 6th period and the 15th group in the periodic table, so it has 83 electrons.
14Step 2: Write the condensed electron configuration
Bismuth's condensed electron configuration is:
\[ \mathrm{[Xe]\, 6s^2\, 4f^{14}\, 5d^{10}\, 6p^3} \]
15Step 3: Determine the number of unpaired electrons
There are 3 unpaired electrons in the 6p orbital.
(f) Sg (Seaborgium)
16Step 1: Find the location in the periodic table
Seaborgium is in the 7th period and the 6th group in the periodic table, so it has 106 electrons.
17Step 2: Write the condensed electron configuration
Seaborgium's condensed electron configuration is:
\[ \mathrm{[Rn]\, 7s^2\, 5f^{14}\, 6d^4} \]
18Step 3: Determine the number of unpaired electrons
There are 4 unpaired electrons in the 6d orbital.
Key Concepts
The Periodic Table and Electron ConfigurationUnpaired Electrons and Chemical ReactivityGround State Electron Configuration
The Periodic Table and Electron Configuration
The periodic table is a comprehensive chart that organizes elements based on their atomic structure and properties. It is divided into rows called periods and columns known as groups or families. More than just a display of elements, the periodic table is a powerful tool for predicting an element's characteristics, including its electron configuration.
Electron configuration refers to the distribution of electrons in an atom's orbitals. It is structured following the principles of quantum mechanics, with each position holding a specific energy level. As you navigate the table from left to right, electrons fill lower-energy orbitals first, moving to higher ones as needed. This is known as the Aufbau principle, which is vital for understanding an element's reactivity and bonding capabilities.
The periodic table is thus integral to determining an atom's electron configuration. For example, Bromine (Br), found in the 4th period and the 17th group, uses its position to indicate its electron configuration is \[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^5} \]. This configuration shows the use of shorthand notation which starts with the noble gas in the previous period (in this case, Argon [Ar]) and proceeds to outline the electrons that have been added beyond this noble gas configuration.
Electron configuration refers to the distribution of electrons in an atom's orbitals. It is structured following the principles of quantum mechanics, with each position holding a specific energy level. As you navigate the table from left to right, electrons fill lower-energy orbitals first, moving to higher ones as needed. This is known as the Aufbau principle, which is vital for understanding an element's reactivity and bonding capabilities.
The periodic table is thus integral to determining an atom's electron configuration. For example, Bromine (Br), found in the 4th period and the 17th group, uses its position to indicate its electron configuration is \[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^5} \]. This configuration shows the use of shorthand notation which starts with the noble gas in the previous period (in this case, Argon [Ar]) and proceeds to outline the electrons that have been added beyond this noble gas configuration.
Unpaired Electrons and Chemical Reactivity
Unpaired electrons play a critical role in the chemical reactivity and magnetic properties of an element. They are the electrons in an atom’s orbitals that are not part of an electron pair. Atoms seek stability, often through interactions that either share or transfer these unpaired electrons to complete their outermost energy levels, known as valence shells.
For instance, in the case of Gallium (Ga), the electron configuration is \[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^1} \], indicating one unpaired electron in the 4p orbital. This single unpaired electron is what can make Gallium reactive as it seeks to pair up to achieve a more stable state. As the number of unpaired electrons increases, the element may exhibit stronger magnetic properties and higher reactivity, making these unpaired electrons a point of interest when studying an element's behavior in chemical reactions.
Understanding the presence of unpaired electrons can help in predicting and explaining the bonding patterns of different elements, as seen with Antimony (Sb) which, with a condensed configuration of \[ \mathrm{[Kr]\, 5s^2\, 4d^{10}\, 5p^3} \], has three unpaired electrons in the 5p orbital, suggesting a higher propensity for forming covalent bonds with other atoms.
For instance, in the case of Gallium (Ga), the electron configuration is \[ \mathrm{[Ar]\, 4s^2\, 3d^{10}\, 4p^1} \], indicating one unpaired electron in the 4p orbital. This single unpaired electron is what can make Gallium reactive as it seeks to pair up to achieve a more stable state. As the number of unpaired electrons increases, the element may exhibit stronger magnetic properties and higher reactivity, making these unpaired electrons a point of interest when studying an element's behavior in chemical reactions.
Understanding the presence of unpaired electrons can help in predicting and explaining the bonding patterns of different elements, as seen with Antimony (Sb) which, with a condensed configuration of \[ \mathrm{[Kr]\, 5s^2\, 4d^{10}\, 5p^3} \], has three unpaired electrons in the 5p orbital, suggesting a higher propensity for forming covalent bonds with other atoms.
Ground State Electron Configuration
Ground state refers to the lowest energy state of an atom, where all electrons are in the lowest available energy levels. When we talk about ground state electron configurations, we are describing the organization of electrons in an atom’s orbitals when the atom is at its most stable, non-excited state.
The rules guiding the distribution of electrons in an atom's orbitals, such as the Pauli exclusion principle—which states that no two electrons can occupy the same quantum state simultaneously—and Hund's rule—which indicates that electrons must fill each degenerate orbital singly before any orbital is doubly occupied—are used to determine the electron arrangement in the ground state.
For example, Seaborgium (Sg) has a ground state electron configuration of \[ \mathrm{[Rn]\, 7s^2\, 5f^{14}\, 6d^4} \], showing that even for elements with a high atomic number, their ground state configurations follow these principles. Notably, the ground state is essential for predicting an element’s behavior since excited states can be fleeting and less influence the typical reactions and bonds an element may form.
The rules guiding the distribution of electrons in an atom's orbitals, such as the Pauli exclusion principle—which states that no two electrons can occupy the same quantum state simultaneously—and Hund's rule—which indicates that electrons must fill each degenerate orbital singly before any orbital is doubly occupied—are used to determine the electron arrangement in the ground state.
For example, Seaborgium (Sg) has a ground state electron configuration of \[ \mathrm{[Rn]\, 7s^2\, 5f^{14}\, 6d^4} \], showing that even for elements with a high atomic number, their ground state configurations follow these principles. Notably, the ground state is essential for predicting an element’s behavior since excited states can be fleeting and less influence the typical reactions and bonds an element may form.
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