J. D. Lee Solutions for Chapter: Atomic Structure and the Periodic Table, Exercise 1: Exercise 1

How is the Bohr theory of the hydrogen atom different from that of Schrödinger?

What is a radial distribution function? Draw this function for the $1\mathrm{s}, 2\mathrm{s}, 3\mathrm{s}, 2\mathrm{p}, 3\mathrm{p}$ and $4\mathrm{p}$ orbitals in a hydrogen atom.

Explain (a) the Pauli exclusion principle and (b) Hund's rule. Show how these are used to specify the electronic arrangements of the first $20$ elements in the periodic table.

What is an orbital? Draw the shapes of the $2\mathrm{s}, 2{\mathrm{p}}_{\mathrm{x}}, 2{\mathrm{p}}_{\mathrm{y}}, 2{\mathrm{p}}_{\mathrm{z}}, 3{\mathrm{d}}_{\mathrm{xy}}$ and $3{\mathrm{d}}_{{\mathrm{z}}^2}$ orbitals.

Give the names and symbols of the four quantum numbers required to define the energy of electrons in atoms. What do these quantum numbers relate to, and what numerical values are possible for each? Show how the shape of the periodic table is related to these quantum numbers.

The first shell may contain up to $2$ electrons, the second shell up to $8$, the third shell up to $18$ and the fourth shell up to $32$. Explain this arrangement in terms of quantum numbers.

Give the values of the four quantum numbers for each electron in the ground state for (a) the oxygen atom, and (b) the scandium atom. (Use positive values for ${\mathrm{m}}_{\mathrm{l}}$ and ${\mathrm{m}}_{\mathrm{s}}$ first.)

Give the sequence in which the energy levels in an atom are filled with electrons. Write the electronic configurations for the elements of atomic number $6, 11, 17$, $25$ and from this decide to which group in the periodic table each element belongs.