Atomic Energy Levels and Sublevels: Structure and Electron Configuration in Multi-Electron Atoms

TOPIC 2: Energy Levels and Sublevels in Atoms. Multielectron Atoms

1. What is the number of energy sublevels for a given energy level? What is the principal quantum number of an energy level that has 4 sublevels? Provide their letter designations.

2. Which element has three electrons in its atom, each with n = 3 and l = 1? What are the possible values of the magnetic quantum number for them? Must they have antiparallel spins?

3. Specify the quantum numbers n and l for the outer electrons in atoms with atomic numbers 12, 13, and 23.

4. Write the electronic and electron-graphic configurations for atoms with atomic numbers 18 and 63. To which electron family do they belong?

5. Using the Klechkowski rule, explain which atomic orbitals are filled first:

a) 3d or 4p;
b) 4f or 5p;
c) 5p or 6s;
d) 4d or 4f.

6. Write the electronic and electron-graphic configurations for atoms with atomic numbers 27 and 7. How many vacant f-orbitals are in the atoms of these elements?

7. Which of the following electronic configurations are incorrect, and explain why:

a) 1s1 2s2 2p6
b) 1s2 2s2 2p6 3s2 3p5 4s1
c) 1s2 2s2 2p6 3s1
d) 1s2 2s2 2p6 3s2 3p6 3d4
e) 1s2 2s2 2p3
f) 1s2 2s3

9. What are the possible values of the quantum numbers n, l, ml, and ms that describe the electron states in the aluminum atom?

10. What is the maximum number of electrons that can occupy the s-, p-, d-, and f-sublevels? Write the electronic and electron-graphic configuration for the atom with atomic number 51.

11. What is the maximum number of electrons that can occupy the K, L, M, N, O, and P levels? What are quantum numbers?

12. The quantum numbers for the outermost electron of a certain element are: n = 5, l = 0, ml = 0, ms = +1/2. How many vacant 4d-orbitals does the atom of this element have? Write the electronic and electron-graphic configuration of this atom.

13. Write the values of the quantum numbers l, ml, and ms for electrons whose principal quantum numbers are 3 and 4.

14. Determine the atomic number of the element in which:

a) the filling of the 3d orbital is completed;
b) the filling of the 4s orbital is completed;
c) the filling of the 4p orbital begins;
d) the filling of the 4f orbital begins.

15. How many vacant 3d-orbitals do the excited atoms of the following elements have:

a) sulfur;
b) chlorine;
c) phosphorus;
d) vanadium?

16. Indicate the quantum numbers n and l for the outer electrons in atoms with atomic numbers 10, 15, and 33.

17. What is:
    a) the orbital quantum number for sublevels with a capacity of 10 and 14;
    b) the principal quantum number for energy levels with a capacity of 32, 50, and 72?

18. Based on the energy level capacities, show how many levels are present in the electron shells of atoms with 18, 36, 54, and 86 electrons.

19. How many unpaired electrons are present in the ground state atoms of:
    a) magnesium;
    b) aluminum;
    c) carbon;
    d) boron;
    e) sulfur?

20. Write the electronic and electron-graphic configurations of the atoms with atomic numbers 39 and 41. How many vacant d-orbitals do these atoms have?

21. Write the electronic and electron-graphic configurations of atoms with atomic numbers 24 and 33, taking into account that the first has a “drop” of one 4s-electron into the 3d-sublevel. What is the maximum spin value of d-electrons for the first atom and p-electrons for the second atom?

22. Write the electronic configurations of the following elements:
    a) cesium;
    b) bromine;
    c) vanadium;
    d) molybdenum;
    e) iron;
    f) titanium;
    g) calcium;
    h) tin;
    i) chlorine;
    j) bromine;
    k) cobalt;
    l) platinum;
    m) lead;
    n) manganese;
    o) sulfur.

23. How many electrons are present in the energy levels with principal quantum numbers of 2, 3, and 4?

24. How many electrons are in the following sublevels:
    a) 4f and 5d in a lead atom;
    b) 5s and 4d in a cesium atom;
    c) 5d and 4f in a tungsten atom;
    d) 3p and 3d in a cobalt atom;
    e) 3d and 4s in an arsenic atom?

25. How many neutrons are in the nuclei of atoms of the following elements:
    a) phosphorus;
    b) lead;
    c) magnesium;
    d) silicon;
    e) tin;
    f) silver;
    g) bismuth;
    h) cadmium;
    i) iron?

26. What is the maximum valency that can be exhibited by the following elements:
    a) tin;
    b) tungsten;
    c) aluminum;
    d) bismuth;
    e) calcium;
    f) titanium;
    g) oxygen;
    h) fluorine;
    i) chlorine?

27. How many vacant f-orbitals are in the atoms of elements with atomic numbers 57, 68, and 82? Distribute the electrons among the orbitals according to Hund’s rule.

28. Based on the electronic structures of fluorine and chlorine atoms, explain the similarities and differences in their properties.

29. Using the Klechkowski rule, write the electronic configurations of the following elements:
    a) manganese;
    b) chromium;
    c) zirconium;
    d) hafnium.

30. According to Hund’s rule, distribute the electrons among the orbitals for atoms in the ground state of:
    a) phosphorus;
    b) carbon;
    c) manganese;
    d) oxygen;
    e) iron.

31. According to Hund’s rule, distribute the electrons among the orbitals for atoms in the excited state of:
    a) boron;
    b) sulfur;
    c) chlorine.