Chapter 5, Problem 79A

Interpretation Introduction

Interpretation: The ground state of an atom, excited state, and impossible electronic configuration of the element is to be inferred. The element is to identify and explained.

Concept Introduction: Electronic configurations refer to the arrangements of electrons in different orbitals around atoms' nuclei. The Aufbau principle, the Pauli exclusion principle, and Hund's rule are three rules that can be used to determine the electronic configuration of atoms.

Answer to Problem 79A

The ground state of the atom is option (a) $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1$ .

The excited state of the atom is (b) $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}5p^1$ .

The impossible electronic configuration is (c) $1s^{2}2s^{2}2p^{6}3s^{2}3p^7$ .

The element is Potassium.

Explanation of Solution

Electronic configurations refer to the arrangements of electrons in different orbitals around atoms' nuclei.

The Aufbau principle, the Pauli exclusion principle, and Hund's rule are three rules that can be used to determine the electronic configuration of atoms.

The energy levels and symbols for each sub-level occupied by an electron are written for an atom's electrical configuration.

Each sub-level is superscripted with the number of electrons occupied. The number of electrons in an atom is equal to the sum of the superscripts.

The order of orbital filling of the atoms is given as

  $1s,2s,3p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f,6d,7p$

Where, s orbitals accommodate 2 electrons, p orbitals 6 electrons, d orbitals 10 electrons, and f orbitals 14 electrons.

Option (a):

The given electronic configuration is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}5p^1$ .

The electronic configuration is not arranged in order of orbital filling, so it is the excited state of the element.

To find the symbol of the atom, add on the superscripts of the electronic configuration.

  $\begin{array}{c}1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}5p^1=2+2+6+2+6+1\\ =19\end{array}$

The element with atomic number 19 is Potassium. Its symbol is $\text{K}$ .

So, option (a) is the excited state of Potassium.

Option (b):

The given electronic configuration is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1$ .

The electronic configuration is arranged in order of orbital filling, so it is the ground state of the element.

To find the symbol of the atom, add on the superscripts of the electronic configuration.

  $\begin{array}{c}1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1=2+2+6+2+6+1\\ =19\end{array}$

The element with atomic number 19 is Potassium. Its symbol is $\text{K}$ .

So, option (b) is the ground state of Potassium.

Option (c):

The given electronic configuration is $1s^{2}2s^{2}2p^{6}3s^{2}3p^7$ .

The electronic configuration is not possible because the p-orbital has 7 electrons which is not possible.

The p-orbital can accommodate only 6 electrons.

So, option (c) is the impossible electronic configuration.