Chapter 1, Problem 1D.23E

(a)

Interpretation Introduction

Interpretation:

Number of orbitals that can have the given quantum numbers has to be written.

    $n=2,l=1$

Concept Introduction:

There are four set of quantum numbers present for explaining the distribution of electron density in an atom.  They are principal quantum number, angular momentum quantum number, magnetic quantum number and spin quantum number.

    $\begin{array}{cccc}\text{Name}& \text{Symbol}& \text{Values}& \text{Specifies}\\ \text{Principal}& \text{n}& \text{1,2,}\mathrm{...}& \text{shell}\\ \text{angular momentum}& \text{l}& \text{0,1,}\mathrm{...}\text{n-1}& \begin{array}{l}\text{subshell:}\\ \text{l}\text{=}\text{0,1,2,3,4}\mathrm{...}\\ \text{s,p,d,f,g}\mathrm{...}\end{array}\\ \text{magnetic}& {\text{m}}_{\text{l}}& \text{l,l-1,}\mathrm{...}\text{,-1}& \text{orbitals}\text{of}\text{shell}\\ \text{spin}& {\text{m}}_{\text{s}}& \text{+}\frac{\text{1}}{\text{2}}\text{,-}\frac{\text{1}}{\text{2}}& \text{spin}\text{state}\end{array}$

For a given value of $\text{n,}$ there will be $\text{n}$ different values for $l.$  And in the case of magnetic quantum number, there will be $\left(2l+1\right)$ different values of $m_l$ present for each values of $l.$

(b)

Interpretation Introduction

Interpretation:

Number of orbitals that can have the given quantum numbers has to be written.

    $n=4,l=2,m_l=-2$

Concept Introduction:

Refer to part (a).

(c)

Interpretation Introduction

Interpretation:

Number of orbitals that can have the given quantum numbers has to be written.

    $n=2$

Concept Introduction:

Refer to part (a).

(d)

Interpretation Introduction

Interpretation:

Number of orbitals that can have the given quantum numbers has to be written.

    $n=3,l=2,m_l=+1$

Concept Introduction:

Refer to part (a).