Problem 77
What are the possible values for the quantum numbers \(n, \ell,\) and \(m_{\ell} ?\)
Problem 79
Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)
Problem 80
Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. \(n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}\) b. \(n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}\) c. \(n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-1\) e. \(n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}\) f. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)
Problem 81
What is the physical significance of the value of \(\psi^{2}\) at a particular point in an atomic orbital?
Problem 82
In defining the sizes of orbitals, why must we use an arbitrary value, such as 90% of the probability of finding an electron in that region?
Problem 88
Give the maximum number of electrons in an atom that can have these quantum numbers: a. \(n=0, \ell=0, m_{\ell}=0\) b. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-\frac{1}{2}\) c. \(n=3, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=2\) e. \(n=1, \ell=0, m_{\ell}=0\)
Problem 89
Draw atomic orbital diagrams representing the ground-state electron configuration for each of the following elements. a. Na b. Co c. Kr How many unpaired electrons are present in each element?
Problem 91
The elements Si, Ga, As, Ge, Al, Cd, S, and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.
Problem 92
Write the expected electron configurations for each of the following atoms: Cl, Sb, Sr, W, Pb, Cf.
Problem 93
How many 4\(d\) electrons would be predicted in the ground state for the following elements? a. zirconium b. cadmium c. iridium d. iron
