Chapter 4, Problem 81E

Interpretation Introduction

(a)

Interpretation:

The three dimensional representation for $1s$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is to be drawn.

Concept introduction:

Electrons in an atom are present in particular orbitals. Sublevels contain orbitals which possess equivalent energy. Maximum two electrons are present in each orbital. The electrons present in $s$ orbital are known as $s$ electrons.

Answer to Problem 81E

The three dimensional representation for $1s$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Explanation of Solution

The energy level possesses a sublevel that contains orbital. The sublevels are named as $s\text{, }p\text{, }d\text{, }f$ and so on. The first energy level contains one sublevel, which is $1s$. The second energy level contains two sublevels, which are $2s$ and $2p$. The third energy level contains three sublevels, which are $3s\text{, }3p$ and $3d$. The fourth energy level contains four sublevels, which are $4s\text{, 4}p\text{, }4d$ and $4f$.

The three dimensional representation for $1s$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Figure 1

Conclusion

The three dimensional representation for $1s$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown in Figure 1.

Interpretation Introduction

(b)

Interpretation:

The three dimensional representation for $2p_x$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is to be drawn.

Concept introduction:

Electrons in an atom are present in particular orbitals. Sublevels contain orbitals which possess equivalent energy. Maximum two electrons are present in each orbital. The electrons present in $s$ orbital are known as $s$ electrons.

Answer to Problem 81E

The three dimensional representation for $2p_x$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Explanation of Solution

The energy level possesses a sublevel that contains orbital. The sublevels are named as $s\text{, }p\text{, }d\text{, }f$ and so on. The first energy level contains one sublevel, which is $1s$. The second energy level contains two sublevels, which are $2s$ and $2p$. The third energy level contains three sublevels, which are $3s\text{, }3p$ and $3d$. The fourth energy level contains four sublevels, which are $4s\text{, 4}p\text{, }4d$ and $4f$.

The three dimensional representation for $2p_x$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Figure 2

Conclusion

The three dimensional representation for $2p_x$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown in Figure 2.

Interpretation Introduction

(c)

Interpretation:

The three dimensional representation for $3p_y$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is to be drawn.

Concept introduction:

Electrons in an atom are present in particular orbitals. Sublevels contain orbitals which possess equivalent energy. Maximum two electrons are present in each orbital. The electrons present in $s$ orbital are known as $s$ electrons.

Answer to Problem 81E

The three dimensional representation for $3p_y$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Explanation of Solution

The energy level possesses a sublevel that contains orbital. The sublevels are named as $s\text{, }p\text{, }d\text{, }f$ and so on. The first energy level contains one sublevel, which is $1s$. The second energy level contains two sublevels, which are $2s$ and $2p$. The third energy level contains three sublevels, which are $3s\text{, }3p$ and $3d$. The fourth energy level contains four sublevels, which are $4s\text{, 4}p\text{, }4d$ and $4f$.

The three dimensional representation for $3p_y$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Figure 3

Conclusion

The three dimensional representation for $3p_y$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown in Figure 3.

Interpretation Introduction

(d)

Interpretation:

The three dimensional representation for $1s$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is to be drawn.

Concept introduction:

Electrons in an atom are present in particular orbitals. Sublevels contain orbitals which possess equivalent energy. Maximum two electrons are present in each orbital. The electrons present in $s$ orbital are known as $s$ electrons.

Answer to Problem 81E

The three dimensional representation for $4p_z$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Explanation of Solution

The energy level possesses a sublevel that contains orbital. The sublevels are named as $s\text{, }p\text{, }d\text{, }f$ and so on. The first energy level contains one sublevel, which is $1s$. The second energy level contains two sublevels, which are $2s$ and $2p$. The third energy level contains three sublevels, which are $3s\text{, }3p$ and $3d$. The fourth energy level contains four sublevels, which are $4s\text{, 4}p\text{, }4d$ and $4f$.

The three dimensional representation for $4p_z$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown below.

Figure 4

Conclusion

The three dimensional representation for $4p_z$ orbital with $x\text{-}$ axis, $y\text{-}$ axis and $z\text{-}$ axis is shown in Figure 4.