Problem 71
For each of the following pairs of hydrogen orbitals indicate which is higher in energy: (a) \(1 s, 2 s ;\) (b) \(2 p, 3 p\); (d) \(3 s, 3 d\); (c) \(3 d_{x y}, 3 d_{y z}\) (e) \(4 f, 5 s\).
Problem 72
Which orbital in each of the following pairs is lower in energy in a many- electron atom: (a) \(2 s, 2 p\); (b) \(3 p, 3 d\) (c) \(3 s, 4 s ;\) d) \(4 d, 5 f\) ?
Problem 73
A \(3 s\) orbital is illustrated here. Using this as a reference to show the relative size of the other four orbitals, answer the following questions.(a) Which orbital has the greatest value of \(n ?\) (b) How many orbitals have a value of \(\ell=1 ?(\mathrm{c})\) How many other orbitals with the same value of \(n\) would have the same general shape as orbital (b)?
Problem 74
What is electron configuration? Describe the roles that the Pauli exclusion principle and Hund's rule play in writing the electron configuration of elements.
Problem 76
State the Aufbau principle, and explain the role it plays in classifying the elements in the periodic table.
Problem 77
Calculate the total number of electrons that can occupy (a) one \(s\) orbital, (b) three \(p\) orbitals, (c) five \(d\) orbitals, (d) seven \(f\) orbitals.
Problem 78
What is the total number of electrons that can be held in all orbitals having the same principal quantum number \(n\) ?
Problem 79
Determine the maximum number of electrons that can be found in each of the following subshells: \(3 s, 3 d, 4 p\), \(4 f, 5 f\).
Problem 80
Indicate the total number of (a) \(p\) electrons in \(\mathrm{N}(Z=7)\) (b) \(s\) electrons in Si \((Z=14)\), and (c) \(3 d\) electrons in \(\mathrm{S}(Z=16)\)
Problem 81
Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why: (a) \(\left(1,1,+\frac{1}{2},-\frac{1}{2}\right)\) (b) \(\left(3,0,-1,+\frac{1}{2}\right)\) (c) \(\left(2,0,+1,+\frac{1}{2}\right)\) (d) \(\left(4,3,-2,+\frac{1}{2}\right)\) (e) (3,2,+1,1)
