Chapter 1, Problem 1D.14E

(a)

Interpretation Introduction

Interpretation:

Number of values of the quantum number $l$ are possible when principal quantum number $\left(n\right)$ equal to $6$ has to be written.

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 $m_l$ allowed for an electron in $5f$ has to be identified.

Concept Introduction:

Refer to part (a).

(c)

Interpretation Introduction

Interpretation:

Number of $m_l$ allowed for an electron in $2s$ has to be identified.

Concept Introduction:

Refer to part (a).

(d)

Interpretation Introduction

Interpretation:

Number of subshells are there in the shell with $n$ value equal to $3$ has to be identified.

Concept Introduction:

Refer to part (a).