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Chapter 6: Problem 58

Give the values for \(n, l,\) and \(m_{l}\) for \((\mathbf{a})\) each orbital in the \(3 p\) subshell, (b) each orbital in the \(4 f\) subshell.

Short Answer

Expert verified
For the 3p subshell, the quantum numbers for each orbital are \((n, l, m_l) = (3, 1, -1), (3, 1, 0),\) and \((3, 1, 1)\). For the 4f subshell, the quantum numbers for each orbital are \((n, l, m_l) = (4, 3, -3), (4, 3, -2), (4, 3, -1), (4, 3, 0), (4, 3, 1), (4, 3, 2),\) and \((4, 3, 3)\).

Step by step solution

01

3p Subshell Quantum Numbers

A 3p subshell has a principal quantum number of \(n=3\). Its azimuthal quantum number is represented by the letter p, which translates to \(l=1\). For the magnetic quantum number \(m_l\), we need to consider possible integer values from \(-l\) to \(+l\): So for the 3p subshell, there are three possible values of \(m_l\): \(-1, 0, 1\) Hence, the quantum numbers for the orbitals in the 3p subshell are: \((n, l, m_l) = (3, 1, -1), (3, 1, 0),\) and \((3, 1, 1)\)
02

4f Subshell Quantum Numbers

A 4f subshell has a principal quantum number of \(n=4\). Its azimuthal quantum number is represented by the letter f, which translates to \(l=3\). For the magnetic quantum number \(m_l\), we need to consider possible integer values from \(-l\) to \(+l\): So for the 4f subshell, there are seven possible values of \(m_l\): \(-3, -2, -1, 0, 1, 2, 3\) Hence, the quantum numbers for the orbitals in the 4f subshell are: \((n, l, m_l) = (4, 3, -3), (4, 3, -2), (4, 3, -1), (4, 3, 0), (4, 3, 1),\) \((4, 3, 2),\) and \((4, 3, 3)\)

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Most popular questions from this chapter

Which of the following represent impossible combinations of \(n\) and $l ?(\mathbf{a}) 1 p,(\mathbf{b}) 4 s,(\mathbf{c}) 5 f,(\mathbf{d}) 2 d$

The electron microscope has been widely used to obtain highly magnified images of biological and other types of materials. When an electron is accelerated through a particular potential field, it attains a speed of $9.47 \times 10^{6} \mathrm{~m} / \mathrm{s}$ What is the characteristic wavelength of this electron? Is the wavelength comparable to the size of atoms?

(a) What is the frequency of radiation that has a wavelength of $10 \mu \mathrm{m}\(, about the size of a bacterium? \)(\mathbf{b})$ What is the wavelength of radiation that has a frequency of $5.50 \times 10^{14} \mathrm{~s}^{-1} ?$ (c) Would the radiations in part (a) or part \((b)\) be visible to the human eye? (d) What distance does electromagnetic radiation travel in \(50.0 \mu \mathrm{s} ?\)

(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is \(2.94 \times 10^{14} \mathrm{~s}^{-1}\). (b) Calculate the energy of a photon of radiation whose wavelength is 413 \(\mathrm{nm} .\) (c) What wavelength of radiation has photons of energy $6.06 \times 10^{-19} \mathrm{~J} ?$

(a) For an He+ ion, do the \(2 s\) and \(2 p\) orbitals have the same energy? If not, which orbital has a lower energy? (b) If we add one electron to form the He atom, would your answer to part (a) change?
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