For the \(K\) shell, the four quantum numbers for each of the two electrons in the \(1 s\) state, in the order of \(n l m_{l} m_{s}\), are \(100 \frac{1}{2}\) and \(100\left(-\frac{1}{2}\right)\). Write the four quantum numbers for all of the electrons in the \(L\) and \(M\) shells, and note which correspond to the \(s, p\), and \(d\) subshells.

Short Answer

Expert verified
Question: List the four quantum numbers for all of the electrons in the L and M shells, and identify which correspond to the s, p, and d subshells. Answer: For the L shell: 1. 2, 0, 0, +1/2 (s subshell) 2. 2, 0, 0, -1/2 (s subshell) 3. 2, 1, -1, +1/2 (p subshell) 4. 2, 1, -1, -1/2 (p subshell) 5. 2, 1, 0, +1/2 (p subshell) 6. 2, 1, 0, -1/2 (p subshell) 7. 2, 1, 1, +1/2 (p subshell) 8. 2, 1, 1, -1/2 (p subshell) For the M shell: 1. 3, 0, 0, +1/2 (s subshell) 2. 3, 0, 0, -1/2 (s subshell) 3. 3, 1, -1, +1/2 (p subshell) 4. 3, 1, -1, -1/2 (p subshell) 5. 3, 1, 0, +1/2 (p subshell) 6. 3, 1, 0, -1/2 (p subshell) 7. 3, 1, 1, +1/2 (p subshell) 8. 3, 1, 1, -1/2 (p subshell) 9. 3, 2, -2, +1/2 (d subshell) 10. 3, 2, -2, -1/2 (d subshell) 11. 3, 2, -1, +1/2 (d subshell) 12. 3, 2, -1, -1/2 (d subshell) 13. 3, 2, 0, +1/2 (d subshell) 14. 3, 2, 0, -1/2 (d subshell) 15. 3, 2, 1, +1/2 (d subshell) 16. 3, 2, 1, -1/2 (d subshell) 17. 3, 2, 2, +1/2 (d subshell) 18. 3, 2, 2, -1/2 (d subshell)

Step by step solution

01

L shell quantum numbers

For the L shell (n=2), l can take values from 0 to n-1, so l can be 0 or 1. We can find the combinations of m_l and m_s for each value of l: - For l=0 (s subshell): - m_l = 0 - m_s = +1/2 or -1/2 - For l=1 (p subshell): - m_l = -1, 0, or 1 - m_s = +1/2 or -1/2 The four quantum numbers for all electrons in the L shell are: 1. 2, 0, 0, +1/2 (s subshell) 2. 2, 0, 0, -1/2 (s subshell) 3. 2, 1, -1, +1/2 (p subshell) 4. 2, 1, -1, -1/2 (p subshell) 5. 2, 1, 0, +1/2 (p subshell) 6. 2, 1, 0, -1/2 (p subshell) 7. 2, 1, 1, +1/2 (p subshell) 8. 2, 1, 1, -1/2 (p subshell)
02

M shell quantum numbers

For the M shell (n=3), l can take values from 0 to n-1, so l can be 0, 1, or 2. We can find the combinations of m_l and m_s for each value of l: - For l=0 (s subshell): - m_l = 0 - m_s = +1/2 or -1/2 - For l=1 (p subshell): - m_l = -1, 0, or 1 - m_s = +1/2 or -1/2 - For l=2 (d subshell): - m_l = -2, -1, 0, 1, or 2 - m_s = +1/2 or -1/2 The four quantum numbers for all electrons in the M shell are: 1. 3, 0, 0, +1/2 (s subshell) 2. 3, 0, 0, -1/2 (s subshell) 3. 3, 1, -1, +1/2 (p subshell) 4. 3, 1, -1, -1/2 (p subshell) 5. 3, 1, 0, +1/2 (p subshell) 6. 3, 1, 0, -1/2 (p subshell) 7. 3, 1, 1, +1/2 (p subshell) 8. 3, 1, 1, -1/2 (p subshell) 9. 3, 2, -2, +1/2 (d subshell) 10. 3, 2, -2, -1/2 (d subshell) 11. 3, 2, -1, +1/2 (d subshell) 12. 3, 2, -1, -1/2 (d subshell) 13. 3, 2, 0, +1/2 (d subshell) 14. 3, 2, 0, -1/2 (d subshell) 15. 3, 2, 1, +1/2 (d subshell) 16. 3, 2, 1, -1/2 (d subshell) 17. 3, 2, 2, +1/2 (d subshell) 18. 3, 2, 2, -1/2 (d subshell)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Without consulting Figure \(2.8\) or Table \(2.2\), determine whether each of the following electron configurations is an inert gas, a halogen, an alkali metal, an alkaline earth metal, or a transition metal. Justify your choices. (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}\) (e) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{5} 5 s^{2}\) (f) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\)

Relative to electrons and electron states, what does each of the four quantum numbers specify?

To what group in the periodic table would an element with atomic number 112 belong?

For an \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)ion pair, attractive and repulsive energies \(E_{A}\) and \(E_{R}\), respectively, depend on the distance between the ions \(r\), according to $$ \begin{aligned} &E_{A}=-\frac{1.436}{r} \\ &E_{R}=\frac{7.32 \times 10^{-6}}{r^{8}} \end{aligned} $$ For these expressions, energies are expressed in electron volts per \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)pair, and \(r\) is the distance in nanometers. The net energy \(E_{N}\) is just the sum of the preceding two expressions. (a) Superimpose on a single plot \(E_{N}, E_{R}\), and \(E_{A}\) versus \(r\) up to \(1.0 \mathrm{~nm}\). (b) On the basis of this plot, determine (i) the equilibrium spacing \(r_{0}\) between the \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\) ions, and (ii) the magnitude of the bonding energy \(E_{0}\) between the two ions. (c) Mathematically determine the \(r_{0}\) and \(E_{0}\) values using the solutions to Problem 2.18, and compare these with the graphical results from part (b).

(a) Briefly cite the main differences among ionic, covalent, and metallic bonding. (b) State the Pauli exclusion principle.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free