Chapter 5, Problem 15STP

Interpretation Introduction

Interpretation: The rules of the arrangement of electrons around the nuclei of atoms need to be explained.

Concept Introduction:

An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

There are three rules for the arrangement of electrons around the nuclei of atoms:

1. Aufbau Principle
2. Hund’s Rule
3. Pauli-Exclusion Principle

The three rules are explained as follows:

Aufbau Principle: According to this principle, electrons are added in atomic orbitals arranged in increasing order of energy.

The increasing order is as follows:

  $s<p<d<f$

Hund’s Rule: According to this rule when electrons are filled in orbitals with the same energy, first all empty orbitals are occupied, and then the paring of electrons takes place.

Pauli-Exclusion Principle: According to this principle, each electron has a unique set of quantum numbers. Thus, even if electrons are occupied in the same orbital, their spin quantum numbers must be different that is they must be paired spins.