Problem 11
What is the maximum number of electrons that can be identified with each of the following sets of quantum numbers? In some cases, the answer may be "none" In such cases, explain why "none" is the correct answer. (a) \(n=4, \ell=3, m_{\ell}=1\) (b) \(n=6, \ell=1, m_{\ell}=-1, m_{\mathrm{s}}=-1 / 2\) (c) \(n=3, \ell=3, m_{c}=-3\)
Problem 12
What is the maximum number of electrons that can be identified with each of the following sets of quantum numbers? In some cases, the answer may be "none." In such cases, explain why "none" is the correct answer. (a) \(n=3\) (b) \(n=3\) and \(\ell=2\) (c) \(n=4, \ell=1, m_{\ell}=-1,\) and \(m_{\mathrm{s}}=+1 / 2\) (d) \(n=5, \ell=0, m_{\ell}=-1, m_{\mathrm{s}}=+1 / 2\)
Problem 13
Depict the electron configuration for magnesium using an orbital box diagram and noble gas notation. Give a complete set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.
Problem 14
Depict the electron configuration for phosphorus using an orbital box diagram and noble gas notation. Give one possible set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.
Problem 15
Using an orbital box diagram and noble gas notation, show the electron configuration of gallium, Ga. Give one possible set of quantum numbers for the highest-energy electron.
Problem 16
Using an orbital box diagram and noble gas notation, show the electron configuration of titanium. Give one possible set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.
Problem 17
The effective nuclear charge, \(Z^{*},\) is the net force of attraction experienced by the outermost electron in an atom. Which of the following statements best describes how \(Z^{*}\) varies among the elements of the second period (Li to \(\mathrm{F}\) )? (a) regular increase from Li to \(\mathrm{F}\) (b) regular decrease from Li to \(\mathrm{F}\) (c) general increase from Li to F, but with exceptions
Problem 18
Which of the following statements correctly describes the value of the effective nuclear charge, \(Z^{*},\) felt by (a) the \(2 s\) electron at a large distance from a Li atom? (i) \(\quad Z^{*}\) equals 1 (ii) \(Z^{*}\) is between 1 and 3 (iii) \(Z^{*}\) equals 3 (b) the \(2 s\) electron at its most probable distance from the nucleus of a Li atom? (i) \(\quad Z^{*}\) equals 1 (ii) \(Z^{*}\) is between 1 and 3 (iii) \(Z^{*}\) equals 3
Problem 19
List the first five orbitals (the five orbitals in an atom at lowest energy) in order of filling, according to the Aufbau principle.
Problem 20
The values of \(n\) and \(\ell\) are useful to determine the order of filling (Aufbau principle). Use \(n\) and \(\ell\) to determine which orbital, \(4 f, 5 d,\) or \(6 s,\) will fill first.
