Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

For the [tex]n=3[/tex] electron shell, which of the following quantum numbers are valid? Check all that apply.

A. [tex]I=3[/tex]

B. [tex]m=3[/tex]

C. [tex]I=0[/tex]

D. [tex]m=-2[/tex]

E. [tex]I=-1[/tex]

F. [tex]m=2[/tex]

Sagot :

GinnyAnswer
To determine the validity of the given quantum numbers for the electron shell with [tex]\( n = 3 \)[/tex]:

First, we must review the constraints on the quantum numbers:
1. The azimuthal quantum number ([tex]\( I \)[/tex]) must satisfy [tex]\( 0 \leq I \leq n - 1 \)[/tex].
For [tex]\( n = 3 \)[/tex], this means [tex]\( I \)[/tex] can be: [tex]\( 0, 1, \)[/tex] or [tex]\( 2 \)[/tex].

2. The magnetic quantum number ([tex]\( m \)[/tex]) must satisfy [tex]\( -I \leq m \leq I \)[/tex].
For each valid [tex]\( I \)[/tex], let's identify the possible values for [tex]\( m \)[/tex]:
- If [tex]\( I = 0 \)[/tex], then [tex]\( m \)[/tex] can only be [tex]\( 0 \)[/tex].
- If [tex]\( I = 1 \)[/tex], then [tex]\( m \)[/tex] can be [tex]\( -1, 0, \)[/tex] or [tex]\( 1 \)[/tex].
- If [tex]\( I = 2 \)[/tex], then [tex]\( m \)[/tex] can be [tex]\( -2, -1, 0, 1, \)[/tex] or [tex]\( 2 \)[/tex].

Now, let's check each of the provided quantum numbers:

1. [tex]\( I = 3 \)[/tex]
- This is not valid because it does not lie within the range [tex]\( 0 \leq I \leq 2 \)[/tex].

2. [tex]\( m = 3 \)[/tex]
- For any [tex]\( I \)[/tex], [tex]\( m \)[/tex] values range from [tex]\( -I \)[/tex] to [tex]\( I \)[/tex]. Since the highest [tex]\( I \)[/tex] can be [tex]\( 2 \)[/tex], [tex]\( m = 3 \)[/tex] is not valid.

3. [tex]\( I = 0 \)[/tex]
- This is valid because [tex]\( 0 \leq I \leq 2 \)[/tex].

4. [tex]\( m = -2 \)[/tex]
- For [tex]\( I = 2 \)[/tex], [tex]\( m = -2 \)[/tex] is valid as it lies within [tex]\( -2 \leq m \leq 2 \)[/tex].

5. [tex]\( I = -1 \)[/tex]
- This is not valid because [tex]\( I \)[/tex] must be non-negative and [tex]\( -1 \)[/tex] is less than [tex]\( 0 \)[/tex].

6. [tex]\( m = 2 \)[/tex]
- For [tex]\( I = 2 \)[/tex], [tex]\( m = 2 \)[/tex] is valid as it lies within [tex]\( -2 \leq m \leq 2 \)[/tex].

Summarizing our findings, the valid quantum numbers from the given options are:
[tex]\[ I = 0 \][/tex]
[tex]\[ m = -2 \][/tex]
[tex]\[ m = 2 \][/tex]

Thus, the valid quantum numbers for the electron shell [tex]\( n = 3 \)[/tex] from the given list are:
[tex]\[ ([0], [-2, 2]). \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.