Chapter 11: Problem 8
Differentiate among the terms energy level, sublevel, and orbital.
Short Answer
Expert verified
In summary, energy levels represent the specific arrangement of electrons in an atom and are described by the principal quantum number (n). Sublevels, determined by the angular momentum quantum number (l), divide energy levels based on the shape of the electron cloud and are represented by the letters 's', 'p', 'd', and 'f'. Orbitals are specific areas within sublevels where there is a high probability of finding electrons with opposite spins and are defined by the magnetic quantum number (m_l).
Step by step solution
01
Understanding Energy Level
Energy level, also known as the electron shell, is the specific arrangement of electrons in an atom. In an atom, electrons are distributed among different energy levels around the nucleus. These energy levels can be described by the principal quantum number (n), which is always a positive integer. The higher the value of n, the larger the energy level, and the farther it is from the nucleus.
Each energy level can hold up to 2n^2 electrons, and the energy levels are generally represented by the integer values 1, 2, 3, and so on. For example, the first energy level (n = 1) can hold up to 2 electrons, the second energy level (n = 2) can hold up to 8 electrons, and so on.
02
Understanding Sublevel
A sublevel is a division of the energy level based on the shape of the electron cloud. The sublevels are denoted by the angular momentum quantum number (l), which has integer values from 0 to n-1, where n is the principal quantum number of the corresponding energy level.
There are four types of sublevels, represented by the letters 's', 'p', 'd', and 'f'. These sublevels indicate different shapes and orientations of the electron cloud in the energy level. Each type of sublevel can hold a specific number of electrons: 's' can hold 2 electrons, 'p' can hold 6 electrons, 'd' can hold 10 electrons, and 'f' can hold 14 electrons.
For example, the first energy level (n = 1) has only the 's' sublevel, while the second energy level (n = 2) has both 's' and 'p' sublevels.
03
Understanding Orbital
An orbital is a specific area in a sublevel in which there is a high probability of finding an electron. Each orbital can hold a maximum of 2 electrons, with opposite spins. The magnetic quantum number (m_l) determines the number of orbitals in a sublevel and their orientation in space, and it has integer values ranging from -l to +l, where l is the angular momentum quantum number of the corresponding sublevel.
For the 's' sublevel, there is only one orbital, called the 's' orbital. For the 'p' sublevel, there are three orbitals, called 'p_x', 'p_y', and 'p_z'. For the 'd' sublevel, there are five orbitals, and for the 'f' sublevel, there are seven orbitals.
In summary, energy levels are related to the principal quantum number (n) and can be divided into sublevels, which are determined by the angular momentum quantum number (l). Each sublevel can be further divided into orbitals, based on the magnetic quantum number (m_l). These orbitals are the specific areas where electrons with opposite spins can be found.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Energy Level
Energy levels, also known as electron shells, serve as the fundamental building blocks of the atomic structure. Visualize these levels as layers or shells surrounding an atom's nucleus. Each energy level is designated by the principal quantum number, represented by \( n \), which indicates its distance from the nucleus. The larger the value of \( n \), the farther the energy level is from the nucleus, and consequently, the higher its energy.
Each energy level has a specific capacity to hold electrons, which can be calculated using the formula \( 2n^2 \). For example:
Each energy level has a specific capacity to hold electrons, which can be calculated using the formula \( 2n^2 \). For example:
- The first energy level \( (n = 1) \) can hold up to 2 electrons.
- The second energy level \( (n = 2) \) can hold up to 8 electrons.
- The third energy level \( (n = 3) \) can accommodate up to 18 electrons.
Sublevel
Sublevels introduce a more nuanced division within energy levels, providing deeper insight into the arrangement of electrons. These sublevels are shaped by the angular momentum quantum number, denoted as \( l \). The value of \( l \) can range from 0 to \( n-1 \), where \( n \) is the principal quantum number of the energy level.
There are four recognized types of sublevels:
There are four recognized types of sublevels:
- 's' sublevel, which has a spherical shape and can hold 2 electrons.
- 'p' sublevel, with a dumbbell shape, can accommodate 6 electrons.
- 'd' sublevel, more complex in shape, can hold 10 electrons.
- 'f' sublevel, which is even more intricate, can contain 14 electrons.
Orbital
Orbital refers to a specific region within a sublevel where there is a high likelihood of finding an electron. Orbitals provide a more precise location for electron presence than sublevels do. Each orbital can accommodate up to 2 electrons, which spin in opposite directions.
The orientation and quantity of these orbitals within a sublevel are determined by the magnetic quantum number, \( m_l \), which can have values between \(-l\) and \(+l\), where \( l \) is the angular momentum quantum number.
The orientation and quantity of these orbitals within a sublevel are determined by the magnetic quantum number, \( m_l \), which can have values between \(-l\) and \(+l\), where \( l \) is the angular momentum quantum number.
- The 's' sublevel has 1 orbital: the spherical 's' orbital.
- The 'p' sublevel contains 3 orbitals: 'p_x', 'p_y', and 'p_z'.
- In the 'd' sublevel, there are 5 distinct orbitals.
- The 'f' sublevel boasts 7 different orbitals.
Quantum Numbers
Quantum numbers are essential "coordinates" that describe the unique quantum state of an electron within an atom. Think of them as addresses that define an electron's position and energy level. There are four primary quantum numbers:
- The Principal quantum number, \( n \), indicates the energy level or shell and determines the electron's distance from the nucleus.
- The Angular momentum quantum number, \( l \), specifies the sublevel and shape of the electron cloud, ranging from 0 to \( n-1 \).
- The Magnetic quantum number, \( m_l \), describes the specific orbital within a sublevel, offering the number of orbitals and their orientation.
- The Spin quantum number dictates the electron's spin direction, either +1/2 or -1/2, further accommodating two electrons per orbital with opposite spins.