Chapter 7, Problem 7.70QP

State which of the following sets of quantum numbers would be possible and which impossible for an electron in an atom.

1. a n = 2, I = 0, m_i = 0, $m_s=+\frac{1}{2}$
2. b n = 1, I = 1, m_i = 0, $m_s=+\frac{1}{2}$
3. c n = 0, I = 0, m_i = 0, $m_s=-\frac{1}{2}$
4. d n = 2, I = 1, m_i = −1, $m_s=+\frac{1}{2}$
5. e n = 2, I = 1, m_i = −2, $m_s=+\frac{1}{3}$

Interpretation Introduction

Interpretation:

The permissible and not permissible quantum number from the given set of quantum numbers has to be identified.

Concept introduction:

Principal Quantum Number(n): In an atom, theelectron 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. The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

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 7.70QP

(a)

Permissible

Explanation of Solution

To identify: The given set of quantum numbers are permissible or not.

The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

The possible values of  Spin Quantum Numbers are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.

The given set of quantum numbers follows the above possible values.  Thus, the given set is permissible.

Interpretation Introduction

Interpretation:

The permissible and not permissible quantum number from the given set of quantum numbers has to be identified.

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. The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

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 7.70QP

(b)

Not permissible.

Explanation of Solution

To identify: The given set of quantum numbers are permissible or not.

The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

But in the given set the $\text{l}\text{=}1$.  Thus, the given set is not permissible.

Interpretation Introduction

Interpretation:

The permissible and not permissible quantum number from the given set of quantum numbers has to be identified.

Concept introduction:

Principal Quantum Number(n): In an atom, theelectron 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. The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

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 7.70QP

(c)

Not permissible

Explanation of Solution

To identify: The given set of quantum numbers are permissible or not.

The principal quantum number n cannot be zero.  But in the given set the ${\text{m}}_{\text{l}}\text{=}\text{+3}$.  Thus, the given set is not permissible.

Interpretation Introduction

Interpretation:

The permissible and not permissible quantum number from the given set of quantum numbers has to be identified.

Concept introduction:

Principal Quantum Number(n): In an atom, theelectron 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. The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

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 7.70QP

(d)

Permissible

Explanation of Solution

To identify: The given set of quantum numbers are permissible or not.

The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

The possible values of Spin Quantum Numbers are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.

The given set of quantum numbers follows the above possible values.  Thus, the given set is permissible.

Interpretation Introduction

Interpretation:

The permissible and not permissible quantum number from the given set of quantum numbers has to be identified.

Concept introduction:

Principal Quantum Number(n): In an atom, theelectron 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. The possible values ofangular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

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 7.70QP

(e)

Not permissible

Explanation of Solution

To identify: The given set of quantum numbers are permissible or not.

Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.

For $\text{l}\text{=}1$, the ${\text{m}}_{\text{l}}\text{can}\text{be}\text{-1,}\text{0,}\text{+1}$.  But in the given set the ${\text{m}}_{\text{l}}\text{=}-2$.  Thus, the given set is not permissible.