Chapter #8 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 3rd Edition

 

1. A lithium atom has three electrons. Allow the electrons to interact with each other and the nucleus. Label each electron’s spin and angular momentum. List all the possible interactions. Get solution

1q. Explain in terms of the electron shell configuration why it is dangerous to throw sodium into water. Get solution

2. For all the elements through neon, list the electron descriptions in their ground state using n/ notation (for example, helium is 1s2). Get solution

2q. Why are the inert gases in gaseous form at room temperature? Why doesn’t helium at atmospheric pressure form a solid at any temperature? Why are the inert gases in gaseous form at room temperature? Why doesn’t helium at atmospheric pressure form a solid at any temperature? Get solution

3. How many subshells are in the following shells: L, N, and O? Get solution

3q. The alkali metals have the lowest ionization energies (Figure 8.3), yet they have the largest atomic radii (Figure 8.4). Is this consistent? Explain. Figure 8.3 ... Get solution

4. What electron configuration would you expect ... for the first excited state of argon and krypton? Get solution

4q. Why are the elements with good electrical conductivities also generally good thermal conductors? Get solution

5. Using Table 8.1 and Figure 8.2 write down the electron configuration ... of the following elements: potassium, vanadium, selenium, zirconium, samarium, and uranium. Reference of table 8.1,figure 8.2 ... ... Get solution

5q. Boron, carbon, and aluminum are not part of the alkalis or alkaline earths, yet they are generally good electrical conductors. Explain. Get solution

6. Use Figure 8.2 to list all the (a) inert gases, (b) alkalis, and (c) alkaline earths. ... Get solution

6q. The alkali metals have the lowest ionization energies (Figure 8.3), yet they have the largest atomic radii (Figure 8.4). Is this consistent? Explain. Figure 8.3 ... Figure 8.4 ... Get solution

7. The 3s state of Na has an energy of -5.14 eV. Determine the effective nuclear charge. Get solution

7q. List four compounds that you believe should be strongly bound. Explain why. Get solution

8. List the quantum numbers ... for all the electrons in a nitrogen atom. Get solution

8q. Explain why the transition metals have good thermal and electrical conductivities. Get solution

9. What atoms have the configuration (a) ... ... Get solution

9q. Why do the alkaline earths have low resistivities? Get solution

10. What are the electronic configurations for the ground states of the elements Pd, Hf, and Sb? Get solution

10q. Why is there no spin-orbit splitting for the ground state of hydrogen? Get solution

11. What atoms have the configuration ... ... Get solution

11q. Is it possible for both atoms in a hydrogen molecule to be in the (1, 0, 0, -1/2) state? Explain. Get solution

12. If the zirconium atom ground state has S = 1 and L = 3, what are the permissible values of J? Write the spectroscopic notation for these possible values of S, L, and J. Which one of these is likely to represent the ground state? Get solution

12q. Discuss in your own words the differences between L and /, between m/ and ms, and between Jz and mj. Get solution

13. Using the information in Table 8.2, determine the ground state spectroscopic symbol for gallium. Reference of table 8.2 ... Get solution

13q. Why do Rydberg atoms live so long? (Hint: Consider the selection rules and the values of their quantum numbers.) Get solution

14. List all the elements through calcium that you would expect not to have a spin-orbit interaction that splits the ground-state energy. Explain. Get solution

14q. Discuss whether the atomic state represented by 32D7/2 exists, and give reasons. Get solution

15. For the hydrogen atom in the 3d excited state find the possible values of ... Give the term notation for each possible configuration. Get solution

16. What are S, L, and J for the following states: 1S0, 2D5/2, 5F1, 3F4? Get solution

17. What are the possible values of Jz for the 82G7/2 state? Get solution

18. (a) What are the possible values of Jz for the 62F7/2 state? (b) Determine the minimum angle between the total angular momentum vector and the z axis for this state. Get solution

19. Explain why the spectroscopic term symbol for lithium in the ground state is 2S1/2. Get solution

20. What is the spectroscopic term symbol for aluminum in its ground state? Explain. Get solution

21. The 4P state in potassium is split by its spin-orbit interaction into the 4P3/2 (λ = 766.41 nm) and 4P1/2 (λ = 769.90 nm) states. (The wavelengths are for the transitions to the ground state.) Calculate the spin orbit energy splitting and the internal magnetic field causing the splitting. Get solution

22. Draw the energy-level diagram for the states of carbon discussed in Example 8.9. Draw lines between states that have allowed transitions and list ΔL, ΔS, and ΔJ. ... ... Get solution

23. An n = 2 shell (L shell) has a 2s state and two 2p states split by the spin-orbit interaction. Careful measurements of the Kα x-ray (n = 2 ...n = 1) transition reveal only two spectral lines. Explain. Get solution

24. What is the energy difference between a spin-up state and spin-down state for an electron in an s state the magnetic field is 1.7 T? Get solution

25. Which of the following elements can have either (or both) singlet and triplet states and which have neither: He, Al, Ca, Sr? Explain. Get solution

26. If the minimum angle between the total angular momentum vector and the z axis is 32.3° (in a single electron atom), what is the total angular momentum quantum number? Get solution

27. Use the Biot-Savart law to find the magnetic field in the frame of an electron circling a nucleus of charge Ze. If the velocity of the electron around the nucleus is ... and the position vector of the proton with respect to the electron is ..., show that the magnetic field at the electron is ... Get solution

28. Use the internal magnetic field of the previous problem to show that the potential energy of the spin magnetic moment μs interacting with ... is given by ... There is an additional factor of 1/2 to be added from relativistic effects called the Thomas factor. Get solution

29. The difference between the 2P3/2 and 2P1/2 doublet in hydrogen due to the spin-orbit splitting is 4.5 × 10-5 eV. (a) Compare this with the potential energy given in the preceding problem. (b) Compare this with a more complete calculation giving the potential energy as ... where α is the fine-structure constant, α ... 1/137. Get solution

30. For which L and S values does an atom exhibit the normal Zeeman effect? Does this apply to both ground and excited states? Can an atom exhibit both the normal and anomalous Zeeman effects? Get solution

31. Derive Equations (8.22) and (8.23). First find the average value of ... and .... Use ... ... ... ... Get solution

32. In the early 1900s the normal Zeeman effect was useful to determine the electron's e/m if Planck's constant was assumed known. Calcium is an clement that exhibits the normal Zeeman effect. The difference be-. tween adjacent components of the spectral lines is observed to be 0.013 nm for ... nm when calcium is placed in a magnetic field of 1.5 T. From these data calculate the value of ... and compare with the accepted value today. Calculate e/m assuming the known value of .... Get solution

33. Calculate the Landé g factor for an atom with a single (a) s electron, (b) p electron, (c) d electron. Get solution

34. An atom with the states 2G9/2 and 2H11/2 is placed in a weak magnetic field. Draw the energy levels and indicate the possible allowed transitions between the two states. Get solution

35. Repeat the preceding problem for 3P1 and 3D2 states. Get solution

36. With no magnetic field, the spectral line representing the transition from the ... state in sodium has the wavelength 589.76 nm (see Figure 8.16). This is one of the two strong yellow lines in sodium. Calculate the difference in wavelength be-tween the shortest and longest wavelength between these two states when placed in a magnetic field of 0.50 T. ... Get solution

37. When sodium in the ... state is placed in a magnetic field of 0.50 T, the energy level splits into four levels (see Figure 8.16). Calculate the energy difference between these levels. ... Get solution

38g. (a) Write down the configurations for the ground states of calcium and aluminum. (b) What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom. Get solution

39g. (a) Write down the configurations for the ground states of the ionized ions ... (b) What_ are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom. Get solution


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