Chapter 5, Problem 44QRT

Assign a correct set of four quantum numbers for

1. (a) Each electron in a nitrogen atom.
2. (b) The valence electron in a sodium atom.
3. (c) A 3d electron in a nickel atom.

Interpretation Introduction

Interpretation:

A correct set of four quantum numbers for each electron in nitrogen atom has to be given.

Concept Introduction:

Principal Quantum Number (n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n)

Angular Momentum Quantum Number (l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.   Angular momentum quantum number is also known as Azimuthal quantum number.  The possible values of angular momentum quantum number are between $\text{0}\text{and}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

Magnetic Quantum Number (${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientations in space.  Any integer between $\text{-l and +l}$ is the probable values of magnetic quantum number.   For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.   For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$. 

Spin Quantum Number (${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.

Explanation of Solution

The electronic configuration of nitrogen atom is given by

    ${\text{1s}}^{\text{2}}{\text{ 2s}}^{\text{2}}{\text{ 2p}}^{\text{3}}$

The arrangement of electrons in nitrogen atom is

    

First electron in 1s orbital:  $\text{n}\text{=}\text{1,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0,}\text{and}\text{s}\text{=}\text{+}\frac{\text{1}}{\text{2}}$

Second electron in 2s orbital:  $\text{n}\text{=}\text{1,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0,}\text{and}\text{s}\text{=}-\frac{\text{1}}{\text{2}}$

First electron in 2s orbital:  $\text{n}\text{=}2\text{,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0,}\text{and}\text{s}\text{=}\text{+}\frac{\text{1}}{\text{2}}$

Second electron in 2s orbital:  $\text{n}\text{=}2\text{,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0,}\text{and}\text{s}\text{=}-\frac{\text{1}}{\text{2}}$

First electron in 2p orbital:  $\text{n}\text{=}2\text{,}\text{l}\text{=}1\text{,}{\text{m}}_{\text{l}}\text{=}+1\text{,}\text{and}\text{s}\text{=}+\frac{\text{1}}{\text{2}}$

Second electron in 2p orbital:  $\text{n}\text{=}2\text{,}\text{l}\text{=}1\text{,}{\text{m}}_{\text{l}}\text{=}0\text{,}\text{and}\text{s}\text{=}+\frac{\text{1}}{\text{2}}$

Third electron in 2p orbital:  $\text{n}\text{=}2\text{,}\text{l}\text{=}1\text{,}{\text{m}}_{\text{l}}\text{=}-1\text{,}\text{and}\text{s}\text{=}+\frac{\text{1}}{\text{2}}$

Interpretation Introduction

Interpretation:

A correct set of four quantum numbers for valence $\text{3s}$ electron in sodium atom has to be given.

Concept Introduction:

Refer to part (a)

Explanation of Solution

The electronic configuration of sodium atom is given by

    ${\text{1s}}^{\text{2}}{\text{ 2s}}^{\text{2}}{\text{ 2p}}^{\text{6}}{\text{ 3s}}^{\text{1}}$

The arrangement of valence $\text{3s}$ electron in sodium atom is

    

First electron in $\text{3s}$ orbital:  $\text{n}\text{=}3\text{,}\text{l}\text{=}\text{0,}{\text{m}}_{\text{l}}\text{=}\text{0,}\text{and}\text{s}\text{=}\text{+}\frac{\text{1}}{\text{2}}$

Interpretation Introduction

Interpretation:

A correct set of four quantum numbers for a $\text{3d}$ electron in nickel atom has to be given.

Concept Introduction:

Refer to part (a)

Explanation of Solution

The electronic configuration of nickel atom is given by

    ${\text{1s}}^{\text{2}}{\text{ 2s}}^{\text{2}}{\text{ 2p}}^{\text{6}}{\text{ 3s}}^{\text{2}}{\text{ 3p}}^{\text{6}}{\text{ 4s}}^{\text{2}}{\text{ 3d}}^{\text{8}}$

The arrangement of a $\text{3d}$ electron in nickel atom is

    

First electron in $\text{3d}$ orbital:  $\text{n}\text{=}3\text{,}\text{l}\text{=}2\text{,}{\text{m}}_{\text{l}}\text{=}+2\text{,}\text{and}\text{s}\text{=}\text{+}\frac{\text{1}}{\text{2}}$