Chapter 7, Problem 10PS

a)

Interpretation Introduction

Interpretation:

The electronic configuration of Plutonium (Pu) has to be predicted using the noble gas and (s, p, d, f) orbital notation methods.  

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Explanation of Solution

The electron configuration is,

$\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Plutonium}\text{(Pu)}\text{=94}\\ \text{Complete (spdf)}\text{notation}\text{of}\text{(Pu)}\text{=}{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^{\text{2}}{\text{3p}}^{\text{6}}{\text{3d}}^{\text{10}}{\text{4s}}^{\text{2}}{\text{4p}}^{\text{6}}{\text{4d}}^{\text{10}}\\ {\text{5s}}^{\text{2}}{\text{5p}}^{\text{6}}{\text{4f}}^{\text{14}}{\text{5d}}^{\text{10}}{\text{6s}}^{\text{2}}{\text{6p}}^{\text{6}}{\text{5f}}^{\text{6}}{\text{6d}}^{\text{0}}{\text{7s}}^{\text{2}}\\ \text{Orbital filling method}=\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^{\text{2}}{\text{3p}}^6\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ 3{\text{d}}^{10}4{\text{s}}^{2}4{\text{p}}^6\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ 4{\text{d}}^{10}5{\text{s}}^2{\text{5p}}^{\text{6}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{4f}}^{\text{14}}{\text{5d}}^{\text{3}}{\text{6s}}^2\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{\uparrow \downarrow }\\ 6{\text{p}}^{\text{6}}{\text{5f}}^{\text{6}}{\text{7s}}^{\text{2}}\\ spdf\text{with noble gas notation}=[\text{Rn}]5{\text{f}}^6{\text{7s}}^{\text{2}}[\because \text{Atomic}\text{number}\text{of}\text{Radon}=86]\\ \text{Orbital}\text{box}\text{notation }\text{= [Rn]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{\uparrow \downarrow }\\ {\text{5f}}^{\text{6}}{\text{6d}}^{\text{0}}7{\text{s}}^2\end{array}$

The electron configuration is,$[\text{Rn}]5{\text{f}}^6{\text{7s}}^{\text{2}}$

b)

Interpretation Introduction

Interpretation:

The electronic configuration of Curium (Cm) has to be derived using the noble gas and (s, p, d, f) orbital notation methods.  

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Explanation of Solution

The electron configuration is,

    $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Curium}\text{(Cm)}\text{=96}\\ \text{Complete (spdf)}\text{notation}\text{of}\text{(Cm)}\text{=}{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^{\text{2}}{\text{3p}}^{\text{6}}{\text{3d}}^{\text{10}}{\text{4s}}^{\text{2}}{\text{4p}}^{\text{6}}{\text{4d}}^{\text{10}}\\ {\text{5s}}^{\text{2}}{\text{5p}}^{\text{6}}{\text{4f}}^{\text{14}}{\text{5d}}^{\text{10}}{\text{6s}}^{\text{2}}{\text{6p}}^{\text{6}}{\text{5f}}^{\text{7}}{\text{6d}}^{\text{1}}{\text{7s}}^{\text{2}}\\ \text{Orbital filling method}=\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^{\text{2}}{\text{3p}}^6\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ 3{\text{d}}^{10}4{\text{s}}^{2}4{\text{p}}^6\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ 4{\text{d}}^{10}5{\text{s}}^2{\text{5p}}^{\text{6}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{4f}}^{\text{14}}{\text{5d}}^{10}{\text{6s}}^2\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}\boxed{\uparrow \downarrow }\\ 6{\text{p}}^{\text{6}}{\text{5f}}^7{\text{6d}}^{\text{1}}{\text{7s}}^{\text{2}}\\ spdf\text{with noble gas notation}=\left[\text{Rn}\right]{\text{ 5f}}^{\text{7}}{\text{6d}}^{\text{1}}{\text{7s}}^{\text{2}}[\because \text{Atomic}\text{number}\text{of}\text{Radon}=86]\\ \text{Orbital}\text{box}\text{notation }\text{= [Rn]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}\boxed{\uparrow \downarrow }\\ {\text{5f}}^7{\text{6d}}^{\text{1}}{\text{7s}}^{\text{2}}\end{array}$

The electron configuration is,$\left[\text{Rn}\right]{\text{ 5f}}^{\text{7}}{\text{6d}}^{\text{1}}{\text{7s}}^{\text{2}}$