Chapter 12, Problem 79E

(a)

Interpretation Introduction

Interpretation: Number of electrons possible with $n$ equal to 4 should be counted.

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 quantized 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 $n=4$ , the permitted values of azimuthal quantum number must range from 0 to 3. Therefore $l$ equal to 0,1,2 and 3 are possible. Hence $4s$ , $4p$ , $4d$ and $4f$ that can have one, three, five and seven subshells respectively so total of 32 electrons can be accommodated in $n=3$ .

(b)

Interpretation Introduction

Interpretation: Number of electrons possible for $n=5$ and $m_l=+1$ should be counted.

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 quantized 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 $n=5$ , the permitted values of azimuthal quantum number must range from 0 to 4. Therefore $l$ equal to 0,1,2, 3 and 4 are possible. However, $m_l=+1$ is associated with one unique orbital for each possible value of $l$ . Thus five orbitals are possible with $n=5$ and $m_l=+1$ , each of these can have two electrons and so total of 10electrons can be accommodated.

(c)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=5$ and $m_s=+\text{1/2}$ should be counted.

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 quantized 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 $n=5$ the permitted values of azimuthal quantum number must range from 0 to 4. Therefore $l$ equal to 0,1,2,3 and 4 are possible. Hence $5s$ , $5p$ , $5d$ , $5g$ and $5f$ hat can have one, three, five, seven and nine subshells respectively so total of 50 electrons can be accommodated in $n=5$ .However,half of these will have $m_s=-\text{1/2}$ and other half will have $m_s=+\text{1/2}$ . Hence 25 electrons are possible for $n=5$ and $m_s=+\text{1/2}$ .

(d)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=3$ and $l=\text{2}$ should be counted.

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 quantized 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 $n=3$ , the permitted values of azimuthal quantum number must range from 0 to 2. Therefore $l$ equal to 0,1,2 and 3 are possible. For a particular value such as $l$ equal to 2, $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-2$ to $+2$ . Thus each orbital has two electrons add up to 10 electrons for $n=3$ and $l=\text{2}$ .

(e)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=2$ and $l=1$ should be counted.

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 quantized 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 $n=2$ , the permitted values of azimuthal quantum number must range from 0 to 1. Therefore $l$ equal to 0 and 1 are possible. For a particular value such as $l=1$ , $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-1$ to $+1$ .Each orbital with two electrons add up to 6 electrons for $n=2$ and $l=1$ .

(f)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=0$ , $l=0$ and $m_l=0$ should be counted.

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 quantized 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

There is no possibility of $n=0$ as principal quantum number can only take values from 1 onwards. So no electrons can be added for the set $n=0$ , $l=0$ and $m_l=0$ .

(g)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=2$ , $l=1$ , $m_l=-1$ and $m_s=-\text{1/2}$ should be counted.

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 quantized 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 $n=2$ , the permitted values of azimuthal quantum number must range from 0 to 1. For a particular value such as $l=1$ , $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ can range from $-1$ to $+1$ .For $m_l=-1$ a unique orbital is assigned and this can only have one electron with spin $-\text{1/2}$ , therefore one electron can come in $n=2$ , $l=1$ , $m_l=-1$ and $m_s=-\text{1/2}$ .

(h)

Interpretation Introduction

Interpretation: Number of electrons possible for $n=3$ and $m_s=+\text{1/2}$ should be counted.

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 quantized 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 $n=3$ , the permitted values of azimuthal quantum number must range from 0 to 2. Therefore $l$ equal to 0,1and 1are possible. Hence $3s$ , $3p$ and $3d$ hat can have one, three, five, subshells respectively so total of 18 electrons can be accommodated in $n=3$ .However,half of these will have $m_s=-\text{1/2}$ and other half will have $m_s=+\text{1/2}$ . Hence 9 electrons are possible for $n=5$ and $m_s=+\text{1/2}$ .

(i)

Interpretation Introduction

Interpretation: Number of electrons possible for $n=2$ and $l=\text{2}$ should be counted.

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 quantized 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 $n=2$ , the permitted values of azimuthal quantum number must range from 0 to 1. Thus $l=\text{2}$ is not possible so no electron can be filled for such set.

(j)

Interpretation Introduction

Interpretation:Number of electrons possible for $n=1$ , $l=0$ and $m_l=0$ should be counted.

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 quantized 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 $n=1$ , the permitted values of azimuthal quantum number can take only value of 0. For a particular value such as $l=0$ , $m_l$ ranges from $-l$ to $+l$ so values of $m_l$ is 0.For $m_l=0$ a unique orbital is assigned and this can have 2 electrons, therefore,two electronscan come in $n=1$ , $l=0$ and $m_l=0$ .