Chapter 12, Problem 66E

(a)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 3, $l$ equal to 3, $m_l$ equal to 0 and $m_s$ equal to $-\text{1/2}$ form correct set or not should be identified and reason behind it should be given.

Concept introduction: There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n$ equal to 3 the permitted values of azimuthal quantum number must range from 0 to 2. Therefore $l$ equal to 3 is not possible and hence the set indicated is incorrect.

The correct set should comprise of either of sets $n=3$ , $l=2$ , $m_l=0$ and $m_s=-\text{1/2}$ ;

  $n=3$ , $l=1$ , $m_l=0$ and $m_s=-\text{1/2}$ and $n=3$ , $l=0$ , $m_l=0$ and $m_s=-\text{1/2}$ .

(b)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 4, $l$ equal to 3, $m_l$ equal to 2 and $m_s$ equal to $-\text{1/2}$ form a correct set or not should be identified and reason behind it should be given.

Concept introduction:There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n$ equal to 4 the permitted values of azimuthal quantum number must range from 0 to 3. Therefore $l$ equal to 3 is possible and allowed.

Since $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-3$ to 3. Thus $m_l$ equal to 2 is also allowed and hence the set indicated is correct.

(c)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 4, $l$ equal to 1, $m_l$ equal to 1 and $m_s$ equal to $-\text{1/2}$ form a correct set or not should be identified and reason behind it should be given.

Concept introduction:There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n=4$ the permitted values of azimuthal quantum number must range from 0 to 3. Therefore $l=1$ is possible and allowed.

Since $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-1$ to 1. Thus $m_l=1$ is also allowed and hence the set indicated is correct.

(d)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 2, $l$ equal to 1, $m_l$ equal to $-\text{1}$ and $m_s$ equal to $-\text{1}$ form a correct set or not should be identified and reason behind it should be given.

Concept introduction:There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n=2$ the permitted values of azimuthal quantum number must range from 0 to 1. Therefore $l=1$ is possible and allowed.

Since $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-1$ to $+1$ . Thus $m_l=-1$ is also allowed, however spin quantum number can only assume values $m_s=+\text{1/2}$ or $m_s=-\text{1/2}$ therefore whole set indicated is not allowed and is incorrect.

(e)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 5, $l$ equal to $-\text{4}$ , $m_l$ equal to 2 and $m_s$ equal to $+\text{1/}2$ form a correct set or not should be identified and reason behind it should be given.

Concept introduction:There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n=5$ the permitted values of azimuthal quantum number must range from 0 to 4. Therefore $l=-4$ is not possible.

Since $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-4$ to $+4$ . Thus $m_l=2$ is also allowed, $m_s=+\text{1/2}$ is allowed but the set as whole is incorrect.

(f)

Interpretation Introduction

Interpretation: Whether set of quantum numbers that include $n$ equal to 3, $l$ equal to 1, $m_l$ equal to 2 and $m_s$ equal to $-\text{1/}2$ form a correct set or not should be identified and reason behind it should be given.

Concept introduction:There are four quantum numbers that serve basis of quantum aspects related to size, position, orientation, and spin associated with an electron.

Principal quantum number depicted as $n$ determines size and energy of a particular shell. It may have values from $n=1,2,3$ and so on.

Azimuthal quantum number describes shape and determines orbital angular momentum associated with a particular orbital. It is characterized by values $l$ equal to 0 for s-orbital, $l$ equal to 1 for p-orbital, $l$ equal to 2 for d-orbital and $l$ equal to 3 for f-orbital orbitals and so on.

Magnetic quantum number determines orientation of certain orbital. Its values range from $-l$ to $+l$ . Each of such orbital gas quantize values of angular momentum that is determined from values of $l$ .

Spin quantum numbers help to predict intrinsic spin associated with electron. It can take only two values $m_s$ equal to $+\text{1/2}$ or $m_s$ equal to $-\text{1/2}$ .

Explanation of Solution

For a given value of principal quantum number $n$ allowed values of $l$ range from 0 to $n-1$ , therefore for $n=3$ the permitted values of azimuthal quantum number must range from 0 to 2. Therefore $l=1$ is possible and allowed.

Since $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-1$ to $+1$ . Thus $m_l=2$ is not allowed, spin quantum number can also assume values of $m_s=-\text{1/2}$ therefore whole set indicated is not allowed and is incorrect.