Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 41 - Atomic Physics - Exercises and Problems - Page 1207: 7

Answer

When $n = 1$, there are 2 quantum states. When $n = 2$, there are 8 quantum states. When $n = 3$, there are 18 quantum states.

Work Step by Step

When $n = 1$: $n = 1, l=0, m = 0, m_s = -\frac{1}{2}$ $n = 1, l=0, m = 0, m_s = \frac{1}{2}$ There are 2 quantum states. When $n = 2$: $n = 2, l=0, m = 0, m_s = -\frac{1}{2}$ $n = 2, l=0, m = 0, m_s = \frac{1}{2}$ $n = 2, l=1, m = -1, m_s = -\frac{1}{2}$ $n = 2, l=1, m = -1, m_s = \frac{1}{2}$ $n = 2, l=1, m = 0, m_s = -\frac{1}{2}$ $n = 2, l=1, m = 0, m_s = \frac{1}{2}$ $n = 2, l=1, m = 1, m_s = -\frac{1}{2}$ $n = 2, l=1, m = 1, m_s = \frac{1}{2}$ There are 8 quantum states. When $n = 3$: $n = 3, l=0, m = 0, m_s = -\frac{1}{2}$ $n = 3, l=0, m = 0, m_s = \frac{1}{2}$ $n = 3, l=1, m = -1, m_s = -\frac{1}{2}$ $n = 3, l=1, m = -1, m_s = \frac{1}{2}$ $n = 3, l=1, m = 0, m_s = -\frac{1}{2}$ $n = 3, l=1, m = 0, m_s = \frac{1}{2}$ $n = 3, l=1, m = 1, m_s = -\frac{1}{2}$ $n = 3, l=1, m = 1, m_s = \frac{1}{2}$ $n = 3, l=2, m = -2, m_s = -\frac{1}{2}$ $n = 3, l=2, m = -2, m_s = \frac{1}{2}$ $n = 3, l=2, m = -1, m_s = -\frac{1}{2}$ $n = 3, l=2, m = -1, m_s = \frac{1}{2}$ $n = 3, l=2, m = 0, m_s = -\frac{1}{2}$ $n = 3, l=2, m = 0, m_s = \frac{1}{2}$ $n = 3, l=2, m = 1, m_s = -\frac{1}{2}$ $n = 3, l=2, m = 1, m_s = \frac{1}{2}$ $n = 3, l=2, m = 2, m_s = -\frac{1}{2}$ $n = 3, l=2, m = 2, m_s = \frac{1}{2}$ There are 18 quantum states.
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