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Chapter 6: Problem 22

What type of electron orbital (i.e., s, \(\mathrm{p}, \mathrm{d}\), or \(\mathrm{f}\) ) is designated by (a) \(\mathrm{n}=2, \ell=1, \mathrm{~m}_{\ell}=-1 ?\) (b) \(\mathbf{n}=1, \ell=0, \mathbf{m}_{\ell}=0 ?\) (c) \(\mathrm{n}=5, \ell=2, \mathrm{~m}_{\ell}=2 ?\)

Short Answer

Expert verified
Question: Identify the electron orbital type for each of the given sets of quantum numbers: a) n=2, l=1, m_l=-1 b) n=1, l=0, m_l=0 c) n=5, l=2, m_l=2 Answer: a) p-orbital b) s-orbital c) d-orbital

Step by step solution

01

Case (a): n=2, l=1, m_l=-1.

We have \(\ell = 1\), so this quantum number corresponds to a p-orbital. Therefore, the electron orbital type for this case is p.
02

Case (b): n=1, l=0, m_l=0.

We have \(\ell = 0\), so this quantum number corresponds to an s-orbital. Therefore, the electron orbital type for this case is s.
03

Case (c): n=5, l=2, m_l=2.

We have \(\ell = 2\), so this quantum number corresponds to a d-orbital. Therefore, the electron orbital type for this case is d.

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Most popular questions from this chapter

What are the possible values for \(\mathbf{m}_{\ell}\) for (a) the \(\mathrm{p}\) sublevel? (b) the \(\mathrm{f}\) sublevel? (c) all sublevels where \(\mathbf{n}=3\) ?

For the Pfund series, \(\mathbf{n}_{\mathrm{lo}}=5\). (a) Calculate the wavelength in nanometers of a transition from \(\mathbf{n}=7\) to \(\mathrm{n}=5 .\) (b) In what region of the spectrum are these lines formed?

Give the number of unpaired electrons in an atom of (a) mercury (b) manganese (c) magnesium

The energy of any one-electron species in its nth state \((\mathbf{n}=\) principal quantum number) is given by \(E=-B Z^{2} / \mathbf{n}^{2}\), where \(Z\) is the charge on the nucleus and \(B\) is \(2.180 \times 10^{-18} \mathrm{~J}\). Find the ionization energy of the \(\mathrm{Li}^{2+}\) ion in its first excited state in kilojoules per mole.

For the following pairs of orbitals, indicate which is higher in energy in a many-electron atom. (a) \(3 \mathrm{~s}\) or \(2 \mathrm{p}\) (b) 4 s or \(4 \mathrm{~d}\) (c) \(4 \mathrm{f}\) or \(6 \mathrm{~s}\) (d) 1 s or \(2 \mathrm{~s}\)
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