Chapter 7, Problem 7.68QP

(a)

Interpretation Introduction

Interpretation:

The orbital which is lower in energy in many electron atoms should be identified in the given pairs of orbitals.

Concept Introduction:

Energy of an orbital in a many electron atom depends on both the values of principle quantum number (n) and angular momentum quantum number (l).  For a given value of principle quantum number (n), the energy of orbital increases with increasing value of the angular momentum quantum number (l) in a many electron atom.

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).

To find: Identify the orbital which is lower in energy in the given pair 2s, 2p orbitals of many electron atoms

Find the value of ‘n’

The principle quantum number (n) of the 2s, 2p orbitals is 2.  Find the value of ‘l’

(b)

Interpretation Introduction

Interpretation:

The orbital which is lower in energy in many electron atoms should be identified in the given pairs of orbitals.

Concept Introduction:

Energy of an orbital in a many electron atom depends on both the values of principle quantum number (n) and angular momentum quantum number (l).  For a given value of principle quantum number (n), the energy of orbital increases with increasing value of the angular momentum quantum number (l) in a many electron atom.

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).

To find: Identify the orbital which is lower in energy in the given pair 3p, 3d orbitals of many electron atoms

Find the value of ‘n’

The principle quantum number (n) of the 3p, 3d orbitals is 3.  Find the value of ‘l’

(c)

Interpretation Introduction

Interpretation:

The orbital which is lower in energy in many electron atoms should be identified in the given pairs of orbitals.

Concept Introduction:

Energy of an orbital in a many electron atom depends on both the values of principle quantum number (n) and angular momentum quantum number (l).  For a given value of principle quantum number (n), the energy of orbital increases with increasing value of the angular momentum quantum number (l) in a many electron atom.

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).

To find: Identify the orbital which is lower in energy in the given pair 3s, 4s orbitals of many electron atoms Find the value of ‘n’

The principle quantum number (n) of the 3s orbital is 3 whereas the principle quantum number (n) of the 4s orbital is 4.  Hence 3s orbital is lower in energy than 4s orbital as the 3s orbital has the lower value of ‘n’ than 4s orbital. Find the value of ‘l’

(d)

Interpretation Introduction

Interpretation:

The orbital which is lower in energy in many electron atoms should be identified in the given pairs of orbitals.

Concept Introduction:

Energy of an orbital in a many electron atom depends on both the values of principle quantum number (n) and angular momentum quantum number (l).  For a given value of principle quantum number (n), the energy of orbital increases with increasing value of the angular momentum quantum number (l) in a many electron atom.

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).

To find: Identify the orbital which is lower in energy in the given pair 4d, 5f orbitals of many electron atoms Find the value of ‘n’

The principle quantum number (n) of the 4d orbital is 4 whereas the principle quantum number (n) of the 5f orbital is 5.  Hence 4d orbital is lower in energy than 5f orbital as the 4d orbital has the lower value of ‘n’ than 5f orbital.  Find the value of ‘l’