Chapter 15, Problem 1DE

(a)

Interpretation Introduction

To determine: The similarities of and differences between the $\text{1s}$ and $\text{2s}$ orbitals of the hydrogen atom.

Answer to Problem 1DE

Solution: They have similar shape but differ in size and number of radial nodes.

Explanation of Solution

In the designation of an orbital the number that is the principal quantum number $n$ gives the shell number and the letter that corresponds to the angular momentum quantum number $l$ gives the subshell.

The shell number decides the size of an orbital and the subshell defines its shape.

Now, $\text{s}$ subshell means that the shape of orbital is spherical. So, both $\text{1s}$ and $\text{2s}$ orbitals are spherical in shape. As $n$ increase size of orbital increases and number of radial nodes also increase as number of radial nodes $=n-1$ .

So $\text{1s}$ orbital has $1-1=0$ radial node while $\text{2s}$ orbital has $2-1=1$ radial node. Also, $1\text{s}$ orbital is smaller in size than $\text{2s}$ orbital.

Conclusion

They have similar shape but differ in size and number of radial nodes.

(b)

Interpretation Introduction

To determine: The directional character of $\text{2p}$ orbital and comparison in directional characteristic of the ${\text{p}}_x$ and ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}$ orbitals.

Answer to Problem 1DE

Solution: The directional character of $\text{2p}$ orbital means that electron density is concentrated in two regions on either side of the nucleus. A ${\text{p}}_x$ orbital is directed along the x-axis while the lobes of a ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}$ orbital lie along the x and y-axes.

Explanation of Solution

The directional character of $\text{2p}$ orbital means that electron density in a $p$ orbital is not uniform around the nucleus and is concentrated in two regions on either side of the nucleus.

A ${\text{p}}_x$ orbital is dumbbell shaped whereas ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}$ orbital is four leaf clover shaped because it has four lobes. A ${\text{p}}_x$ orbital is oriented along the x-axis while the lobes of ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}$ orbital lie along the x and y-axes.

Conclusion

The directional character of a $\text{2p}$ orbital means that electron density is concentrated in two regions on either side of the nucleus. A ${\text{p}}_x$ orbital is directed along the x-axis while the lobes of ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}$ orbital lie along the x and y-axes.

(c)

Interpretation Introduction

To determine: The comparison between average distance from nucleus of $\text{2s}$ orbital and $\text{3s}$ orbital.

Answer to Problem 1DE

Solution: The average distance of $\text{2s}$ orbital from the nucleus is less as compared to that of $\text{3s}$ orbital.

Explanation of Solution

The distance from the nucleus of an orbital is defined by principal quantum number $n$ . As $n$ increases size of the orbital increases and number of radial nodes also increase as number of radial nodes $=n-1$ . So, the average distance of $\text{2s}$ orbital from the nucleus is less as compared to that of $\text{3s}$ orbital.

Conclusion

The average distance of $\text{2s}$ orbital from the nucleus is less as compared to that of $\text{3s}$ orbital.

(d)

Interpretation Introduction

To determine: The increasing energy order of the orbitals $\text{4f,}\text{6s,}\text{3d,}\text{1s,}\text{2p}$ .

Answer to Problem 1DE

Solution: The increasing energy order of the orbitals is given below.

$\text{1s}<\text{2p}<\text{3d}<\text{6s}<\text{4f}$

Explanation of Solution

The energy of orbital increases with increase in principal quantum number $n$ but the subshells $\text{s,p,d,f}$ also differ in energy as $\text{s}<\text{p}<\text{d}<\text{f}$ . So, theorder of increasing energy of given orbitals is,

$\text{1s}<\text{2p}<\text{3d}<\text{6s}<\text{4f}$

Conclusion

The increasing energy order of the orbitals is $\text{1s}<\text{2p}<\text{3d}<\text{6s}<\text{4f}$ .