Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 6 - Electronic Structure of Atoms - Exercises: 6.56b

Answer

For $n=5$, there are 5 possible values for $l$ and 25 possible values for $m_l$.

Work Step by Step

*NOTES TO REMEMBER: - The angular momentum quantum number $l$ can have values from $0$ to $(nāˆ’1)$ for each value of $n$. - The magnetic quantum number $m_l$ can have integral values from $āˆ’l$ to $l$, including $0$. For $n=5$, there are 5 possible values for $l$ $(0, 1, 2, 3, 4)$. - For $l=0$, there is 1 possible value for $m_l$ $(0)$. - For $l=1$, there are 3 possible values for $m_l$ $(-1, 0, 1)$. - For $l=2$, there are 5 possible values for $m_l$ $(-2, -1, 0, 1, 2)$. - For $l=3$, there are 7 possible values for $m_l$ $(-3, -2, -1, 0, 1, 2, 3)$. - For $l=4$, there are 9 possible values for $m_l$ $(-4, -3, -2, -1, 0, 1, 2, 3, 4)$. Overall, there are 25 possible values for $m_l$.
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