# Chapter 3, Problem 3.91QP

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### CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933

#### Solutions

Chapter
Section
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### CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933

(a)

Interpretation Introduction

Interpretation:

The relative size of the given four orbitals which is referred with 3s orbital, the greatest value of n in the given orbitals, the orbitals which have a value of l = 1 and the orbitals with the same value of n which have the same general shape as orbital (b) should be identified using the concept of quantum numbers.

Concept Introduction:

Shapes of s, p and d orbitals

All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases.

All p orbitals are dumb-bell in shape.  The three p orbitals (px, py and pz) are identical in size, shape and energy; they differ from one another only in orientation.

All d orbitals (dxy, dyz, dzx, dx2-y2 and dz2) are identical in energy.  They are labeled with subscripts denoting their orientation with respect to the x, y, and z axes and to the planes defined by them.

Quantum Numbers

Quantum numbers are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

Principal Quantum Number (n)

The principal quantum number (n) assigns the size of the orbital and specifies the energy of an electron.  If the value of n is larger, then the average distance of an electron in the orbital from the nucleus will be greater.  Therefore the size of the orbital is large. The principal quantum numbers have the integral values of 1, 2, 3 and so forth and it corresponds to the quantum number in Bohr’s model of the hydrogen atom.  If all orbitals have the same value of ‘n’, they are said to be in the same shell (level).  The total number of orbitals for a given n value is n2.  As the value of ‘n’ increases, the energy of the electron also increases.

Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) explains the shape of the atomic orbital.  The values of l are integers which depend on the value of the principal quantum number, n.  For a given value of n, the possible values of l range are from 0 to n − 1.  If n = 1, there is only one possible value of l (l=0).  If n = 2, there are two values of l: 0 and 1.  If n = 3, there are three values of l: 0, 1, and 2.  The value of l is selected by the letters s, p, d, and f.  If l = 0, we have an s orbital; if l = 1, we have a p orbital; if l = 2, we have a d orbital and finally if l = 3, we have a f orbital.  A collection of orbitals with the same value of n is called a shell.  One or more orbitals with the same n and l values are referred to a subshell (sublevel).  The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f).

(b)

Interpretation Introduction

Interpretation:

The relative size of the given four orbitals which is referred with 3s orbital, the greatest value of n in the given orbitals, the orbitals which have a value of l = 1 and the orbitals with the same value of n which have the same general shape as orbital (b) should be identified using the concept of quantum numbers.

Concept Introduction:

Shapes of s, p and d orbitals

All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases.

All p orbitals are dumb-bell in shape.  The three p orbitals (px, py and pz) are identical in size, shape and energy; they differ from one another only in orientation.

All d orbitals (dxy, dyz, dzx, dx2-y2 and dz2) are identical in energy.  They are labeled with subscripts denoting their orientation with respect to the x, y, and z axes and to the planes defined by them.

Quantum Numbers

Quantum numbers are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

Principal Quantum Number (n)

The principal quantum number (n) assigns the size of the orbital and specifies the energy of an electron.  If the value of n is larger, then the average distance of an electron in the orbital from the nucleus will be greater.  Therefore the size of the orbital is large. The principal quantum numbers have the integral values of 1, 2, 3 and so forth and it corresponds to the quantum number in Bohr’s model of the hydrogen atom.  If all orbitals have the same value of ‘n’, they are said to be in the same shell (level).  The total number of orbitals for a given n value is n2.  As the value of ‘n’ increases, the energy of the electron also increases.

Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) explains the shape of the atomic orbital.  The values of l are integers which depend on the value of the principal quantum number, n.  For a given value of n, the possible values of l range are from 0 to n − 1.  If n = 1, there is only one possible value of l (l=0).  If n = 2, there are two values of l: 0 and 1.  If n = 3, there are three values of l: 0, 1, and 2.  The value of l is selected by the letters s, p, d, and f.  If l = 0, we have an s orbital; if l = 1, we have a p orbital; if l = 2, we have a d orbital and finally if l = 3, we have a f orbital.  A collection of orbitals with the same value of n is called a shell.  One or more orbitals with the same n and l values are referred to a subshell (sublevel).  The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f).

(c) and (d)

Interpretation Introduction

Interpretation:

The relative size of the given four orbitals which is referred with 3s orbital, the greatest value of n in the given orbitals, the orbitals which have a value of l = 1 and the orbitals with the same value of n which have the same general shape as orbital (b) should be identified using the concept of quantum numbers.

Concept Introduction:

Shapes of s, p and d orbitals

All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases.

All p orbitals are dumb-bell in shape.  The three p orbitals (px, py and pz) are identical in size, shape and energy; they differ from one another only in orientation.

All d orbitals (dxy, dyz, dzx, dx2-y2 and dz2) are identical in energy.  They are labeled with subscripts denoting their orientation with respect to the x, y, and z axes and to the planes defined by them.

Quantum Numbers

Quantum numbers are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

Principal Quantum Number (n)

The principal quantum number (n) assigns the size of the orbital and specifies the energy of an electron.  If the value of n is larger, then the average distance of an electron in the orbital from the nucleus will be greater.  Therefore the size of the orbital is large. The principal quantum numbers have the integral values of 1, 2, 3 and so forth and it corresponds to the quantum number in Bohr’s model of the hydrogen atom.  If all orbitals have the same value of ‘n’, they are said to be in the same shell (level).  The total number of orbitals for a given n value is n2.  As the value of ‘n’ increases, the energy of the electron also increases.

Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) explains the shape of the atomic orbital.  The values of l are integers which depend on the value of the principal quantum number, n.  For a given value of n, the possible values of l range are from 0 to n − 1.  If n = 1, there is only one possible value of l (l=0).  If n = 2, there are two values of l: 0 and 1.  If n = 3, there are three values of l: 0, 1, and 2.  The value of l is selected by the letters s, p, d, and f.  If l = 0, we have an s orbital; if l = 1, we have a p orbital; if l = 2, we have a d orbital and finally if l = 3, we have a f orbital.  A collection of orbitals with the same value of n is called a shell.  One or more orbitals with the same n and l values are referred to a subshell (sublevel).  The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f).

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