Chapter 7, Problem 7.82QE

Interpretation Introduction

Interpretation:

The four quantum numbers for the highest energy electron in ground state of scandium atom have to be determined.

Concept Introduction:

The acceptable wave function is characterized by a set of four quantum numbers. These quantum numbers are related to the shape, size of the electron wave and the location of the electron in space.

1. These quantum numbers are represented by $n$, $l$, $m_l$, and $m_s$. The quantum number $n$ is known as principal quantum number and it allowed values are all positive whole numbers. The quantum number $l$ is known as angular momentum quantum number and its allowed values are all positive integer from 0 to $n-1$.

2. The notation of subshell is used to determine by a combination of both principal quantum number and angular quantum number. In notation, numerical values of $n$ is used while value of $l$ denotes the respective subshell. The table for the $l$ values is as follows:

$\begin{array}{cccccccc}l& 0& 1& 2& 3& 4& 5& 6\\ \text{Subshell}& s& p& d& f& g& h& i\end{array}$

3. The quantum number $m_l$ is known as the magnetic quantum number. It tells about the orbitals present in the subshell and its allowed values lie between $-l$ to $+l$ include 0.

4. The quantum number $m_s$ is known as the electron spin quantum number. It represents the spin of the electron and its allowed values are $+\text{1/2}$ and $-\text{1/2}$.

The electronic configuration is defined as the distribution of electrons in various atomic orbitals of the atom. The electrons that are present in an outermost orbital are known as valence electrons whereas those present in the orbitals with lower quantum numbers are called core electrons. The general outer electronic configuration of $s\text{ block}$ elements is $n{s}^{1-2}$, that of $p\text{ block}$ elements is $n{s}^{2}n{p}^{1-6}$, that of $d\text{ block}$ elements is $\left(n-1\right)d^{1-10}n{s}^{0-2}$ and that of $f\text{ block}$ elements is $\left(n-2\right)f^{1-14}\left(n-1\right)d^{0-10}n{s}^2$.

Electrons are filled in orbitals in accordance with three rules: Aufbau principle, Hund’s rule, and Pauli’s exclusion principle. Aufbau principle states that electrons are filled in the orbitals from lower to higher energy level as follows:

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

Hund’s rule states that initially each orbital is singly occupied and then pairing occurs and Pauli’s exclusion principle states that the spin of two electrons in one orbital is always different.