Chemistry 9th Edition

Published by Cengage Learning
ISBN 10: 1133611095
ISBN 13: 978-1-13361-109-7

Chapter 7 - Atomic Structure and Periodicity - Exercises - Page 344: 71

Answer

$n$ can be any integer greater than zero. $l$ can be any positive integer (including zero) with a maximum value that is one less than that of $n$ such that the following inequality is true: $l \leq (n-1)$ $m_l$ can be ANY (positive or negative) integer of $l$. In other words, $\pm l$.

Work Step by Step

$n$ is the principal quantum number and represents the energy level of an orbital. Since there is no energy level less than 1, $n$ can be any number greater than zero. $l$ is the angular momentum quantum number and represents the sublevel that an orbital is in. $l$ can be zero and any positive integer so long as the following inequality is true: $l ≤ (n-1)$. This means that the maximum value of $l$ is one less than the value of $n$. $m_l$ is the magnetic quantum number and represents the orientation in space of the orbital in comparison of the other orbitals in a certain atom. $m_l$ can have any positive or negative value of $l$ (in other words ranging from±$l, -l < m_l < +l$). We can also represent the value of $m_l$ as an inequality: $|m_l| \leq (n - 1)$ OR $|m_l| = l$
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