What is the maximum number of electrons in an atom that can have the following quantum numbers? Specify the orbitals in which the electrons would be found. (a) n = 2, mS = +; (b) n = 4, ml = +1; (c) n = 3, l = 2; (d) n = 2, l = 0, mS = −; (e) n = 4, l = 3, ml = −2.
(a)
Interpretation:
The maximum number of electrons in an atom which can occupy in all orbitals having the given quantum numbers and the specification of the orbitals should be explained using the concept of quantum numbers.
Concept Introduction:
Quantum Numbers
The distribution of electron density in an atom is defined by Quantum numbers. They are derived from the mathematical solution of Schrodinger’s equation in the hydrogen atom. The four types of quantum numbers are the principal quantum number (
Principal Quantum Number (
The size of an orbital and the energy of an electron are specified by the principal quantum number (
Angular Momentum Quantum Number (
The shape of the atomic orbital is given by the angular momentum quantum number (
Magnetic Quantum Number (
The orientation of the orbital in space is given the magnetic quantum number (
There is one possible
There are three
There are five
There are seven
For a particular
Electron Spin Quantum Number (
For an electron, the orientation of the spin axis is given by it. An electron can spin in two directions. There are two possible ways to represent
Pauli exclusion principle
The two electrons in an atom should not have the four same quantum numbers. Two electrons are occupied in an atomic orbital because there are two possible values of
To find: Count the maximum number of electrons in an atom that can have the quantum number
Answer to Problem 3.123QP
The maximum number of electrons in an atom that can have the quantum number
Explanation of Solution
For a given value of
For a given value of
If
Here,
(b)
Interpretation:
The maximum number of electrons in an atom which can occupy in all orbitals having the given quantum numbers and the specification of the orbitals should be explained using the concept of quantum numbers.
Concept Introduction:
Quantum Numbers
The distribution of electron density in an atom is defined by Quantum numbers. They are derived from the mathematical solution of Schrodinger’s equation in the hydrogen atom. The four types of quantum numbers are the principal quantum number (
Principal Quantum Number (
The size of an orbital and the energy of an electron are specified by the principal quantum number (
Angular Momentum Quantum Number (
The shape of the atomic orbital is given by the angular momentum quantum number (
Magnetic Quantum Number (
The orientation of the orbital in space is given the magnetic quantum number (
There is one possible
There are three
There are five
There are seven
For a particular
Electron Spin Quantum Number (
For an electron, the orientation of the spin axis is given by it. An electron can spin in two directions. There are two possible ways to represent
Pauli exclusion principle
The two electrons in an atom should not have the four same quantum numbers. Two electrons are occupied in an atomic orbital because there are two possible values of
To find: Count the maximum number of electrons in an atom that can have the quantum number
Answer to Problem 3.123QP
The maximum number of electrons in an atom that can have the quantum number
Explanation of Solution
If
Each of
(c)
Interpretation:
The maximum number of electrons in an atom which can occupy in all orbitals having the given quantum numbers and the specification of the orbitals should be explained using the concept of quantum numbers.
Concept Introduction:
Quantum Numbers
The distribution of electron density in an atom is defined by Quantum numbers. They are derived from the mathematical solution of Schrodinger’s equation in the hydrogen atom. The four types of quantum numbers are the principal quantum number (
Principal Quantum Number (
The size of an orbital and the energy of an electron are specified by the principal quantum number (
Angular Momentum Quantum Number (
The shape of the atomic orbital is given by the angular momentum quantum number (
Magnetic Quantum Number (
The orientation of the orbital in space is given the magnetic quantum number (
There is one possible
There are three
There are five
There are seven
For a particular
Electron Spin Quantum Number (
For an electron, the orientation of the spin axis is given by it. An electron can spin in two directions. There are two possible ways to represent
Pauli exclusion principle
The two electrons in an atom should not have the four same quantum numbers. Two electrons are occupied in an atomic orbital because there are two possible values of
To find: Count the maximum number of electrons in an atom that can have the quantum number
Answer to Problem 3.123QP
The maximum number of electrons in an atom that can have the quantum number
Explanation of Solution
If
Each of 3d orbitals occupies two electrons. Hence, 10 electrons are resulted. Therefore, the maximum number of electrons in an atom that can have the quantum number
(d)
Interpretation:
The maximum number of electrons in an atom which can occupy in all orbitals having the given quantum numbers and the specification of the orbitals should be explained using the concept of quantum numbers.
Concept Introduction:
Quantum Numbers
The distribution of electron density in an atom is defined by Quantum numbers. They are derived from the mathematical solution of Schrodinger’s equation in the hydrogen atom. The four types of quantum numbers are the principal quantum number (
Principal Quantum Number (
The size of an orbital and the energy of an electron are specified by the principal quantum number (
Angular Momentum Quantum Number (
The shape of the atomic orbital is given by the angular momentum quantum number (
Magnetic Quantum Number (
The orientation of the orbital in space is given the magnetic quantum number (
There is one possible
There are three
There are five
There are seven
For a particular
Electron Spin Quantum Number (
For an electron, the orientation of the spin axis is given by it. An electron can spin in two directions. There are two possible ways to represent
Pauli exclusion principle
The two electrons in an atom should not have the four same quantum numbers. Two electrons are occupied in an atomic orbital because there are two possible values of
To find: Count the maximum number of electrons in an atom that can have the quantum number
Answer to Problem 3.123QP
The maximum number of electrons in an atom that can have the quantum number
Explanation of Solution
If
Here,
(e)
Interpretation:
The maximum number of electrons in an atom which can occupy in all orbitals having the given quantum numbers and the specification of the orbitals should be explained using the concept of quantum numbers.
Concept Introduction:
Quantum Numbers
The distribution of electron density in an atom is defined by Quantum numbers. They are derived from the mathematical solution of Schrodinger’s equation in the hydrogen atom. The four types of quantum numbers are the principal quantum number (
Principal Quantum Number (
The size of an orbital and the energy of an electron are specified by the principal quantum number (
Angular Momentum Quantum Number (
The shape of the atomic orbital is given by the angular momentum quantum number (
Magnetic Quantum Number (
The orientation of the orbital in space is given the magnetic quantum number (
There is one possible
There are three
There are five
There are seven
For a particular
Electron Spin Quantum Number (
For an electron, the orientation of the spin axis is given by it. An electron can spin in two directions. There are two possible ways to represent
Pauli exclusion principle
The two electrons in an atom should not have the four same quantum numbers. Two electrons are occupied in an atomic orbital because there are two possible values of
To find: Count the maximum number of electrons in an atom that can have the quantum number
Answer to Problem 3.123QP
The maximum number of electrons in an atom that can have the quantum number
Explanation of Solution
If
4f-orbital occupies two electrons. Therefore, the maximum number of electrons in an atom that can have the quantum number
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Chapter 3 Solutions
Chemistry: Atoms First
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