Chapter 8, Problem 8A.8E

(a)

Interpretation Introduction

Interpretation:

The orbital angular momentum, angular node, and radial node of an electron in given orbital have to be determined.

Explanation of Solution

The orbital angular momentum of an electron in 1s orbital is determined as,

    $\begin{array}{l}\text{orbital}\text{angular}\text{momentum}\text{=}\sqrt[]{\text{l(l+1)}}\frac{\text{h}}{\text{2π}}\\ \\ \text{=}\sqrt[]{\text{0(0+1)}}\frac{\text{h}}{\text{2π}}\text{=}\text{0}\end{array}$

The radial and angular nodes are identified as,

    $\begin{array}{l}\text{l}\text{angular}\text{nodes}\text{and}\text{n-l-1}\text{radial}\text{nodes}\\ \\ \text{Hence,}\text{0}\text{angular}\text{node}\text{and}\text{0}\text{radial}\text{node}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The orbital angular momentum, angular node, and radial node of an electron in given orbital have to be determined.

Explanation of Solution

The orbital angular momentum of an electron in 3s orbital is determined as,

    $\begin{array}{l}\text{orbital}\text{angular}\text{momentum}\text{=}\sqrt[]{\text{l(l+1)}}\frac{\text{h}}{\text{2π}}\\ \\ \text{=}\sqrt[]{\text{0(0+1)}}\frac{\text{h}}{\text{2π}}\text{=}\text{0}\end{array}$

The radial and angular nodes are identified as,

    $\begin{array}{l}\text{l}\text{angular}\text{nodes}\text{and}\text{n-l-1}\text{radial}\text{nodes}\\ \\ \text{Hence,}\text{0}\text{angular}\text{node}\text{and}2\text{radial}\text{nodes}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The orbital angular momentum, angular node, and radial node of an electron in given orbital have to be determined.

Explanation of Solution

The orbital angular momentum of an electron in 3d orbital is determined as,

    $\begin{array}{l}\text{orbital}\text{angular}\text{momentum}\text{=}\sqrt[]{\text{l(l+1)}}\frac{\text{h}}{\text{2π}}\\ \\ \text{=}\sqrt[]{\text{2(2+1)}}\frac{\text{h}}{\text{2π}}\text{=}\sqrt{\text{6}}\frac{\text{6}{\text{.62607004 × 10}}^{\text{-34}}{\text{ m}}^{\text{2}}\text{ kg / s}}{\text{2}\text{×}\text{3}\text{.14}}\\ \\ \text{=}\text{2}\text{.58}\text{×}{\text{10}}^{\text{-34}}\text{J}\text{.s}\end{array}$

The radial and angular nodes are identified as,

    $\begin{array}{l}\text{l}\text{angular}\text{nodes}\text{and}\text{n-l-1}\text{radial}\text{nodes}\\ \\ \text{Hence,}2\text{angular}\text{node}\text{and}1\text{radial}\text{node}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The orbital angular momentum, angular node, and radial node of an electron in given orbital have to be determined.

Explanation of Solution

The orbital angular momentum of an electron in 2p orbital is determined as,

    $\begin{array}{l}\text{orbital}\text{angular}\text{momentum}\text{=}\sqrt[]{\text{l(l+1)}}\frac{\text{h}}{\text{2π}}\\ \\ \text{=}\sqrt[]{\text{1(1+1)}}\frac{\text{h}}{\text{2π}}\text{=}\sqrt{2}\frac{\text{6}{\text{.62607004 × 10}}^{\text{-34}}{\text{ m}}^{\text{2}}\text{ kg / s}}{\text{2}\text{×}\text{3}\text{.14}}\\ \\ \text{=}1.\text{49}\text{×}{\text{10}}^{\text{-34}}\text{J}\text{.s}\end{array}$

The radial and angular nodes are identified as,

    $\begin{array}{l}\text{l}\text{angular}\text{nodes}\text{and}\text{n-l-1}\text{radial}\text{nodes}\\ \\ \text{Hence,}1\text{angular}\text{node}\text{and}0\text{radial}\text{node}\end{array}$

(e)

Interpretation Introduction

Interpretation:

The orbital angular momentum, angular node, and radial node of an electron in given orbital have to be determined.

Explanation of Solution

The orbital angular momentum of an electron in 3p orbital is determined as,

    $\begin{array}{l}\text{orbital}\text{angular}\text{momentum}\text{=}\sqrt[]{\text{l(l+1)}}\frac{\text{h}}{\text{2π}}\\ \\ \text{=}\sqrt[]{\text{1(1+1)}}\frac{\text{h}}{\text{2π}}\text{=}\sqrt{2}\frac{\text{6}{\text{.62607004 × 10}}^{\text{-34}}{\text{ m}}^{\text{2}}\text{ kg / s}}{\text{2}\text{×}\text{3}\text{.14}}\\ \\ \text{=}1.\text{49}\text{×}{\text{10}}^{\text{-34}}\text{J}\text{.s}\end{array}$

The radial and angular nodes are identified as,

    $\begin{array}{l}\text{l}\text{angular}\text{nodes}\text{and}\text{n-l-1}\text{radial}\text{nodes}\\ \\ \text{Hence,}1\text{angular}\text{node}\text{and}1\text{radial}\text{node}\end{array}$