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Chapter 7: Problem 52

An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.

Short Answer

Expert verified
Therefore, for an electron at the \(n=3\) energy level, the possible values of \(\ell\) and \(m_{\ell}\) are: for \(\ell = 0\), \(m_{\ell} = 0\); for \(\ell = 1\), \(m_{\ell}\) can be -1, 0, or 1; and for \(\ell = 2\), \(m_{\ell}\) could be -2, -1, 0, 1, or 2.

Step by step solution

01

Identifying the possible values of \(\ell\)

For a given principal quantum number \(n\), the azimuthal quantum number, \(\ell\), can have any integer values from 0 to \(n-1\). In this case, since \(n=3\), \(\ell\) can be either 0, 1, or 2.
02

Identifying the possible values of \(m_{\ell}\) for each \(\ell\)

The magnetic quantum number, \(m_{\ell}\), can have any integer values from \(-\ell\) to \(\ell\). So, when \(\ell = 0\), \(m_{\ell} = 0\); when \(\ell = 1\), \(m_{\ell}\) can be -1, 0, or 1; and when \(\ell = 2\), \(m_{\ell}\) could be -2, -1, 0, 1, or 2.

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Most popular questions from this chapter

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