Chapter 7: Problem 15
Using an orbital box diagram and noble gas notation, show the electron configuration of gallium, Ga. Give one possible set of quantum numbers for the highest-energy electron.
Short Answer
Expert verified
[Ar] 3d^{10} 4s^2 4p^1; Quantum numbers: n=4, l=1, m_l=-1, m_s=+1/2
Step by step solution
01
Determine Atomic Number
Gallium (Ga) has an atomic number of 31, which means it has 31 electrons.
02
Identify Noble Gas Core
The closest noble gas preceding gallium is argon (Ar), which has 18 electrons. Thus, the noble gas notation for gallium starts with [Ar].
03
Continue Electron Configuration Beyond Noble Gas
Beyond argon, add the remaining electrons: 3d has 10 electrons, and 4s has 2 electrons. The 10 electrons fill the 3d orbital, and the 2 electrons fill the 4s orbital. Next, place 1 electron in the 4p orbital.
04
Write Complete Electron Configuration
Put the information together to get the full electron configuration:
[Ar] 3d^{10} 4s^2 4p^1.
05
Orbital Box Diagram
Draw boxes for each sublevel:
- 3d has 5 boxes with 2 arrows each (representing 10 electrons).
- 4s has 1 box with 2 arrows (2 electrons).
- 4p has 3 boxes, but only the first box contains 1 arrow (representing a single electron).
06
Determine Quantum Numbers for Highest-Energy Electron
The highest-energy electron in 4p^1 has the following quantum numbers:
- Principal quantum number, n = 4
- Azimuthal quantum number, l = 1 (p orbital)
- Magnetic quantum number, m_l = -1, 0, or 1 (choose one, e.g., m_l = -1)
- Spin quantum number, m_s = +1/2 or -1/2 (choose one, e.g., m_s = +1/2)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Orbital Box Diagram
The orbital box diagram is a visual way of representing electron configurations. It helps us understand how electrons are distributed within an atom's orbitals. Each box in the diagram represents an orbital, and the arrows inside indicate the electrons occupying these orbitals.
When creating an orbital box diagram for an element, you draw a series of boxes for each type of orbital:
When creating an orbital box diagram for an element, you draw a series of boxes for each type of orbital:
- Subshells have specific numbers of orbitals: s (1 box), p (3 boxes), d (5 boxes), f (7 boxes).
- Arrows in boxes: Each arrow represents an electron. Up and down arrows show paired electrons with opposite spins.
- 3d holds 10 electrons, which means 5 boxes each with two paired arrows.
- 4s holds 2 electrons in a single box.
- 4p starts filling with one electron in the first of its three boxes.
Noble Gas Notation
Noble gas notation is a shorthand method for writing electron configurations. It helps simplify the process by using a noble gas symbol to represent filled electron sub-levels up to that gas.
The steps to use noble gas notation are straightforward:
The steps to use noble gas notation are straightforward:
- Identify the noble gas that precedes your element: This forms the root of the notation. For gallium (Ga), argon (Ar) is the noble gas before it.
- Write the configuration: Start with the noble gas in brackets, then add the configuration beyond it. For Ga, it is [Ar], which represents the first 18 electrons of gallium.
Quantum Numbers
Quantum numbers describe the specific characteristics of electrons within an atom's atom structure. Each electron in an atom is defined by four unique quantum numbers, and these serve to specify its probable location and behavior within the electron cloud.
Here's an overview of the quantum numbers:
Here's an overview of the quantum numbers:
- Principal Quantum Number (n): Indicates the energy level of the electron. For the highest-energy electron in gallium's configuration, this is 4, as its highest occupies the 4p orbital.
- Azimuthal Quantum Number (l): This number describes the shape of the orbital. It is determined by n - 1. For p orbitals, l = 1.
- Magnetic Quantum Number (m_l): Specifies the orientation of the orbital. For p orbitals, m_l can be -1, 0, or +1. In gallium, we choose one, such as m_l = -1.
- Spin Quantum Number (m_s): Indicates the electron's spin direction. This is either +1/2 or -1/2. Again, a choice is made, for instance, m_s = +1/2.