Chapter 7, Problem 7.112QP

For each of the following combinations of quantum numbers, make changes that produce an allowed combination. Count 3 for each change of n, 2 for each change of I, and 1 for each change of m_i. What is the lowest possible count that you can obtain?

1. a n = 3, I = 0, m_i = −2
2. b n = 5, I = 5, m_i = 4
3. c n = 3, I = 3, m_i = −3
4. d n = 5, I = 6, m_i = 3

Interpretation Introduction

Interpretation:

From the given combinations of quantum number, the possible combination has to be given.

Concept introduction:

Principal Quantum Number (n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n)

Angular Momentum Quantum Number (l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.  Angular momentum quantum number is also known as Azimuthal quantum number.

Magnetic Quantum Number ( ${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientation in space.  Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.  For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.  For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$.

Spin Quantum Number ( ${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Answer to Problem 7.112QP

(a)

Corrected set of quantum number is $\text{n}\text{=}\text{3,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0}$.

Explanation of Solution

To give: The possible combination of quantum number.

Given,

$\text{n}\text{=}\text{3,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=-2}$ .

$\text{n}\text{=}3$ indicates the principal quantum number is three.  The possible l values are $0,1,2$. The given set has l value zero.  Finally the possible ${\text{m}}_{\text{l}}$ value for the given l value is zero.

Here the ${\text{m}}_{\text{l}}$ value changes and the count is three.

Corrected set of quantum number: $\text{n}\text{=}\text{3,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0}$.

Interpretation Introduction

Interpretation:

From the given combinations of quantum number, the possible combination has to be given.

Concept introduction:

Principal Quantum Number (n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n)

Angular Momentum Quantum Number (l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.  Angular momentum quantum number is also known as Azimuthal quantum number.

Magnetic Quantum Number ( ${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientation in space.  Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.  For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.  For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$.

Spin Quantum Number ( ${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Answer to Problem 7.112QP

(b)

Corrected set of quantum number is $\text{n}\text{=}5\text{,}\text{l}\text{=}4\text{,}{\text{m}}_{\text{l}}\text{=}\text{4}$.

Explanation of Solution

To give: The possible combination of quantum number.

Given,

$\text{n}\text{=}5\text{,}\text{l}\text{=}5\text{,}{\text{m}}_{\text{l}}\text{=}\text{4}$.

$\text{n}\text{=}5$ indicates the principal quantum number is four .  The possible l values are $\text{0,}\text{1,}\text{2,3}\text{,4}$.  The given set has l value five which is not possible and it is changed to four based on ${\text{m}}_{\text{l}}$ value.  Here the l value changes and the count is two.

Corrected set of quantum number: $\text{n}\text{=}5\text{,}\text{l}\text{=}4\text{,}{\text{m}}_{\text{l}}\text{=}\text{4}$.

Interpretation Introduction

Interpretation:

From the given combinations of quantum number, the possible combination has to be given.

Concept introduction:

Principal Quantum Number (n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n)

Angular Momentum Quantum Number (l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.  Angular momentum quantum number is also known as Azimuthal quantum number.

Magnetic Quantum Number ( ${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientation in space.  Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.  For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.  For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$.

Spin Quantum Number ( ${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Answer to Problem 7.112QP

(c)

Corrected set of quantum number is $\text{n}\text{=}5\text{,}\text{l}\text{=}4\text{,}{\text{m}}_{\text{l}}\text{=}\text{4}$.

Explanation of Solution

To give: The possible combination of quantum number.

Given,

$\text{n}\text{=}\text{3,}\text{l}\text{=}\text{3,}{\text{m}}_{\text{l}}\text{=}\text{-3}$.

$\text{n}\text{=}3$ indicates the principal quantum number is three.  It is changed based on l and ${\text{m}}_{\text{l}}$ values to four.  Then possible l values are $0,1,2,3$.  The given set has l value three which is correct and no need to change.  Here the n value changes and the count is three.

Corrected set of quantum number: $\text{n}\text{=}4\text{,}\text{l}\text{=}\text{3,}{\text{m}}_{\text{l}}\text{=}\text{-3}$.

Interpretation Introduction

Interpretation:

From the given combinations of quantum number, the possible combination has to be given.

Concept introduction:

Principal Quantum Number (n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n)

Angular Momentum Quantum Number (l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.  Angular momentum quantum number is also known as Azimuthal quantum number.

Magnetic Quantum Number ( ${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientation in space.  Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.  For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.  For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$.

Spin Quantum Number ( ${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Answer to Problem 7.112QP

(d)

Corrected set of quantum number is $\text{n}\text{=}5\text{,}\text{l}\text{=}3\text{,}{\text{m}}_{\text{l}}\text{=}\text{3}$.

Explanation of Solution

To give: The possible combination of quantum number.

Given,

$\text{n}\text{=}5\text{,}\text{l}\text{=}6\text{,}{\text{m}}_{\text{l}}\text{=}\text{3}$.

$\text{n}\text{=}5$ indicates the principal quantum number is five .  The possible l values are $\text{0,}\text{1,}\text{2,3}\text{,4}$.  The given set has l value six which is not possible and it is changed to three based on ${\text{m}}_{\text{l}}$ value.  Here the n value changes and the count is three.

Corrected set of quantum number: $\text{n}\text{=}5\text{,}\text{l}\text{=}3\text{,}{\text{m}}_{\text{l}}\text{=}\text{3}$.