Chapter 6, Problem 97QP

Write the ground-state electron configurations for the following elements: $\text{Ge, Fe, Zn, Ni, W, Tl}\text{.}$

Interpretation Introduction

Interpretation:

The ground state electron configurations of the given elements are to be obtained.

Concept introduction:

Aufbau Principle states that every electron occupies the orbitals in the increasing of their energy.

The four steps for writing the ground state electron configuration of an element are shown below:

An electron enters the lowest energy orbital.

A maximum of two electrons can occupy each orbital.

In a degenerate orbital, the electrons do not pair until all the orbitals are occupied with at least one electron.

Electrons occupy the orbitals in the following order:

Noble gas core is used to represent electron configuration of all the elements except hydrogen and helium.

Noble gas core is an abbreviation in an atom’s electron configuration. It replaces the electron configuration of noble gas element most recently precede the element.

Answer to Problem 97QP

Solution:

$\begin{array}{c}\text{Ge: }[\text{Ar}]4s^{2}3d^{10}4p^2\\ \text{Fe: }[\text{Ar}]4s^{2}3d^6\\ \text{Zn: }[\text{Ar}]4s^{2}3d^{10}\\ \text{Ni: }[\text{Ar}]4s^{2}3d^8\\ \text{W: }[\text{Xe}]6s^{2}4f^{14}5d^4\\ \text{Tl: }[\text{Xe}]6s^{2}4f^{14}5d^{10}6p^1\end{array}$

Explanation of Solution

Given information: Ge, Fe, Zn, Ni, W, and Tl elements.

Every electron occupies the orbitals in the increasing order of their energy $\left(1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p\right)$.

The atomic number of the element Ge is $32$. The noble gas core, in this case, is [Ar], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^6$. This core accounts for $18$ electrons, which leaves $14$ electrons to be placed.

Hence, the ground state electronic configuration is $[\text{Ar}]4s^{2}3d^{10}4p^2$.

The atomic number of the element Fe is $26$. The noble gas core, in this case, is [Ar], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^6$. This core accounts for $18$ electrons, which leaves $8$ electrons to be placed.

Hence, the ground state electronic configuration is $[\text{Ar}]4s^{2}3d^6$.

The atomic number of the element Zn is $30$. The noble gas core, in this case, is [Ar], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^6$. This core accounts for $18$ electrons, which leaves $12$ electrons to be placed.

Hence, the ground state electron configuration is $[\text{Ar}]4s^{2}3d^{10}$.

The atomic number of the element Ni is $28$. The noble gas core, in this case, is [Ar], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^6$. This core accounts for $18$ electrons, which leaves $10$ electrons to be placed.

Hence, the ground state electronic configuration is $[\text{Ar}]4s^{2}3d^8$.

The atomic number of the element W is $74$. The noble gas core, in this case, is [Xe], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{6}4d^{10}5s^{2}5p^6$. This core accounts for $54$ electrons, which leaves $20$ electrons to be placed.

Hence, the ground state electronic configuration is $[\text{Xe}]6s^{2}4f^{14}5d^4$.

The atomic number of the element Tl is $81$. The noble gas core, in this case, is [Xe], which is represented by $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{6}4d^{10}5s^{2}5p^6$. This core accounts for $54$ electrons, which leaves $27$ electrons to be placed.

Hence, the ground state electronic configuration is $[\text{Xe}]6s^{2}4f^{14}5d^{10}6p^1$.

Conclusion

The ground state electron configurations of elements (Ge, Fe, Zn, Ni, W, Tl) are as follows:

$\begin{array}{c}\text{Ge: }[\text{Ar}]4s^{2}3d^{10}4p^2\\ \text{Fe: }[\text{Ar}]4s^{2}3d^6\\ \text{Zn: }[\text{Ar}]4s^{2}3d^{10}\\ \text{Ni: }[\text{Ar}]4s^{2}3d^8\\ \text{W: }[\text{Xe}]6s^{2}4f^{14}5d^4\\ \text{Tl: }[\text{Xe}]6s^{2}4f^{14}5d^{10}6p^1\end{array}$