Homework Problems Chapter 8

Last updated
Save as PDF

Page ID: 290609

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Homework Problems

Section 1

Exercise 1

How many microstates exist for the electron configurations

a) p³

b) f²

c) d³

Answer

a) p³- 6!/((6-3)!3!) = 20

b) f²-14!/((14-2)!2!)=91

c) d³-10!/((10-3)!3!)=120

Exercise 2

What is the term symbol for the one term associated with the following electron configurations?

a) p⁶

b) p¹

c) f¹⁴

d) s¹

Answer

a) p⁶ - ¹S

b) p¹ - ²P

c) f¹⁴- ¹S

d) s¹ - ²S

Exercise 3

What is the number of microstates for a

a) ⁵D term

b) ⁴G term

c) ²F term

Answer

a) (2L+1)(2S+1) = 5 x 5 = 25

b) (2L+1)(2S+1) = 9 x 4 = 36

c) (2L+1)(2S+1) = 7 x 2 = 14

Exercise 4

In a triplet term there are

a) only microstates with unpaired electrons.

b) only microstates with paired electrons.

c) microstates with paired and unpaired electrons.

Answer: c) microstates with paired and unpaired electrons.

Exercise 5

In a singlet term there are

a) only microstates with unpaired electrons.

b) only microstates with paired electrons.

c) microstates with paired and unpaired electrons.

Answer: b) only microstates with paired electrons.

Dr. Kai Landskron (Lehigh University). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate.