Chapter 4, Problem 88E

Interpretation Introduction

(a)

Interpretation:

The maximum number of electrons that can be occupied by $1s$ sublevel is to be stated.

Concept introduction:

An atom is made up of three subatomic particles-neutrons, protons, and electrons. Neutrons and protons are present in the nucleus of the atom, whereas electrons are revolving outside the nucleus in an atom. The electrons are arranged in the subshell of atoms according to their energy.

Answer to Problem 88E

The maximum number of electrons that can be occupied by $1s$ sublevel is $2$.

Explanation of Solution

The energy level of the $1s$ sublevel is $1$.

The maximum number of electrons that can be present in a sublevel are independent of their energy levels. Each orbital can contain maximum two electrons in it.

The number of orbitals in $s$ subshell is $1$.

The maximum number of electrons that can be occupied by a sublevel can be represented as shown below.

$N_{\text{e}}=2N_{\text{o}}$

Where,

• $N_{\text{e}}$ represents the maximum number of electrons in a sublevel.

• $N_{\text{o}}$ represents the number of orbitals in the sublevel.

Substitute the value of $N_{\text{o}}$ in the above equation.

$\begin{array}{rll}{N}_{\text{e}}& =& 2\left(1\right)\\ & =& 1\end{array}$

Therefore, the maximum number of electrons that can be occupied by $1s$ sublevel is $2$.

Conclusion

The maximum number of electrons that can be occupied by $1s$ sublevel is $2$.

Interpretation Introduction

(b)

Interpretation:

The maximum number of electrons that can be occupied by $2p$ sublevel is to be stated.

Concept introduction:

An atom is made up of three subatomic particles-neutrons, protons, and electrons. Neutrons and protons are present in the nucleus of the atom, whereas electrons are revolving outside the nucleus in an atom. The electrons are arranged in the subshell of atoms according to their energy.

Answer to Problem 88E

The maximum number of electrons that can be occupied by $2p$ sublevel is $6$.

Explanation of Solution

The energy level of the $2p$ sublevel is $2$.

The maximum number of electron that can be present in a sublevel are independent of their energy levels. Each orbital can contain maximum two electrons in it.

The number of orbitals in $p$ subshell is $3$.

The maximum number of electrons that can be occupied by a sublevel can be represented as shown below.

$N_{\text{e}}=2N_{\text{o}}$

Where,

• $N_{\text{e}}$ represents the maximum number of electrons in a sublevel.

• $N_{\text{o}}$ represents the number of orbitals in the sublevel.

Substitute the value of $N_{\text{o}}$ in the above equation.

$\begin{array}{rll}{N}_{\text{e}}& =& 2\left(3\right)\\ & =& 6\end{array}$

Therefore, the maximum number of electrons that can be occupied by $2p$ sublevel is $6$.

Conclusion

The maximum number of electrons that can be occupied by $2p$ sublevel is $6$.

Interpretation Introduction

(c)

Interpretation:

The maximum number of electrons that can be occupied by $3d$ sublevel is to be stated.

Concept introduction:

An atom is made up of three subatomic particles-neutrons, protons, and electrons. Neutrons and protons are present in the nucleus of the atom, whereas electrons are revolving outside the nucleus in an atom. The electrons are arranged in the subshell of atoms according to their energy.

Answer to Problem 88E

The maximum number of electrons that can be occupied by $3d$ sublevel is $10$.

Explanation of Solution

The energy level of the $3d$ sublevel is $3$.

The maximum number of electrons that can be present in a sublevel are independent of their energy level. Each orbital can contain maximum two electrons in it.

The number of orbitals in $d$ subshell is $5$.

The maximum number of electrons that can be occupied by a sublevel can be represented as shown below.

$N_{\text{e}}=2N_{\text{o}}$

Where,

• $N_{\text{e}}$ represents the maximum number of electrons in a sublevel.

• $N_{\text{o}}$ represents the number of orbitals in the sublevel.

Substitute the value of $N_{\text{o}}$ in the above equation.

$\begin{array}{rll}{N}_{\text{e}}& =& 2\left(5\right)\\ & =& 10\end{array}$

Therefore, the maximum number of electrons that can be occupied by $3d$ orbital is $10$.

Conclusion

The maximum number of electrons that can be occupied by $3d$ sublevel is $10$.

Interpretation Introduction

(d)

Interpretation:

The maximum number of electrons that can be occupied by $4f$ sublevel is to be stated.

Concept introduction:

An atom is made up of three subatomic particles-neutrons, protons, and electrons. Neutrons and protons are present in the nucleus of the atom, whereas electrons are revolving outside the nucleus in an atom. The electrons are arranged in the subshell of atoms according to their energy.

Answer to Problem 88E

The maximum number of electrons that can be occupied by $4f$ sublevel is $14$.

Explanation of Solution

The energy level of the $4f$ sublevel is $4$.

The maximum number of electrons that can be present in a sublevel are independent of their energy level. Each orbital can contain maximum two electrons in it.

The number of orbitals in $f$ subshell is $7$.

The maximum number of electrons that can be occupied by a sublevel can be represented as shown below.

$N_{\text{e}}=2N_{\text{o}}$

Where,

• $N_{\text{e}}$ represents the maximum number of electrons in a sublevel.

• $N_{\text{o}}$ represents the number of orbitals in the sublevel.

Substitute the value of $N_{\text{o}}$ in the above equation.

$\begin{array}{rll}{N}_{\text{e}}& =& 2\left(7\right)\\ & =& 14\end{array}$

Therefore, the maximum number of electrons that can be occupied by $4f$ sublevel is $14$.

Conclusion

The maximum number of electrons that can be occupied by $4f$ sublevel is $14$.