/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 79 Which of the following sets of q... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 79

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)

Short Answer

Expert verified
Sets (b), (c), and (d) are not allowed in the hydrogen atom. Set (b) is incorrect due to \(m_\ell\), set (c) is incorrect due to \(n\), and set (d) is incorrect due to \(\ell\).

Step by step solution

01

Check set (a)

For set (a), we have the following quantum numbers: - \(n=3\) - \(\ell=2\) - \(m_\ell=2\) Since \(n=3\), we have \(\ell = 0, 1, 2\). The condition for \(\ell\) is satisfied. Now for \(\ell=2\), the allowed \(m_\ell\) values are \(-2, -1, 0, 1, 2\). Since \(m_\ell=2\), this set follows all the rules and is allowed.
02

Check set (b)

For set (b), we have the following quantum numbers: - \(n=4\) - \(\ell=3\) - \(m_\ell=4\) Since \(n=4\), we have \(\ell = 0, 1, 2, 3\). The condition for \(\ell\) is satisfied. Now for \(\ell=3\), the allowed \(m_\ell\) values are \(-3, -2, -1, 0, 1, 2, 3\). However, we have \(m_\ell=4\), which is not allowed. Therefore, set (b) is incorrect due to \(m_\ell\).
03

Check set (c)

For set (c), we have the following quantum numbers: - \(n=0\) - \(\ell=0\) - \(m_\ell=0\) Since the principal quantum number (n) starts from 1, the value \(n=0\) is not allowed. Therefore, set (c) is incorrect due to the value of \(n\).
04

Check set (d)

For set (d), we have the following quantum numbers: - \(n=2\) - \(\ell=-1\) - \(m_\ell=1\) Since \(n=2\), we have \(\ell = 0, 1\). Thus, the value \(\ell=-1\) is not allowed. Therefore, set (d) is incorrect due to the value of \(\ell\). #Conclusion#: - Set (a) is allowed. - Set (b) is incorrect due to \(m_\ell\). - Set (c) is incorrect due to \(n\). - Set (d) is incorrect due to \(\ell\).

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