Chemistry 10th Edition

Published by Brooks/Cole Publishing Co.
ISBN 10: 1133610668
ISBN 13: 978-1-13361-066-3

Chapter 4 - The Structure of Atoms - Exercises - Quantum Numbers and Atomic Orbitals - Page 169: 93

Answer

a) $1$, $0$, $0$, $+\frac{1}{2}$, $-\frac{1}{2}$ b) $2$, $1$, $1$, $\frac{1}{2}$ c) Magnetic quantum number has to be either $-2$, $-1$, $0$, $1$ or $2$. It can not be equal to $3$. d) $3$, $2$, $2$, $+\frac{1}{2}$ e) $2$, $1$, $-1$, $+\frac{1}{2}$ or $2$, $1$, $-1$, $-\frac{1}{2}$ f) $3$, $1$, $-1$, $-\frac{1}{2}$ or $3$, $2$, $-1$, $-\frac{1}{2}$

Work Step by Step

a) According to Pauli Exclusion Principle, there can not be 2 electrons in the same orbital and with the same spin quantum number. Therefore, one of the electrons has to have a spin quantum number equal to $-\frac{1}{2}$. b) Since principal quantum number is equal to $2$, angular quantum number can be either $0$ or $1$. If $l=0$, then $m_{l}$ could be only $0$. Since $m_{l}=1$, angular quantum number has to be equal to $1$. c) Magnetic quantum number can be either $-2$, $-1$, $0$, $1$ or $2$, since angular quantum number equals $2$. It can not be equal to $3$. d) Since principal quantum number is equal to $3$ and magnetic is equal to $2$, angular quantum number can be only $2$. e) Spin quantum number can not be equal to $0$. It has to be $+\frac{1}{2}$ or $-\frac{1}{2}$. f) Since principal quantum number is equal to $3$ and magnetic is equal to $-1$, angular quantum number can be only $1$ or $2$.
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