Chapter 14, Problem 87E

(a):

Interpretation Introduction

To determine:

Explanation:

Given The orbital having dumbbell shape.
The orbitals are classified on the basis of their shapes. The orbital having dumbbell shape is the p orbital. The quantum number $l$ for the p orbital is $1$ .

(b)

Explanation:

Given The principle quantum number of the given orbital is $3$ .
The direction of the given orbital is along y axis.
The orbital has dumbbell shape.
The orbital has dumbbell shape means the given orbital is a p orbital and the value of principle quantum number is $3$ means the given orbital is a $3\text{p}$ orbital. The direction of the orbital is specified on the basis of electron density which is along y axis for the given orbital. Therefore, the given orbital is $3{\text{p}}_y$ orbital.

(c):

Interpretation Introduction

To determine: The way to change the magnetic quantum number of the given orbital.