Answered

Join IDNLearn.com and start getting the answers you've been searching for. Our community is here to provide detailed and trustworthy answers to any questions you may have.

Which of the following is not a valid set of quantum numbers?

A. [tex]n=2, \ l=1, \ m=0[/tex]
B. [tex]n=1, \ l=0, \ m=0[/tex]
C. [tex]n=3, \ l=3, \ m=3[/tex]

Sagot :

GinnyAnsweridn
To determine which set of quantum numbers is not valid, we need to review the rules that constrain the quantum numbers:
1. The principal quantum number [tex]\( n \)[/tex] must be a positive integer ([tex]\( n \geq 1 \)[/tex]).
2. The angular momentum quantum number [tex]\( l \)[/tex] must be an integer that satisfies [tex]\( 0 \leq l < n \)[/tex].
3. The magnetic quantum number [tex]\( m \)[/tex] must be an integer that satisfies [tex]\( -l \leq m \leq l \)[/tex].

Let's check each set according to these rules:

1. Set 1: [tex]\( n = 2, l = 1, m = 0 \)[/tex]
- The principal quantum number [tex]\( n = 2 \)[/tex] is a positive integer, which is valid.
- The angular momentum quantum number [tex]\( l = 1 \)[/tex] satisfies [tex]\( 0 \leq l < n \)[/tex] (0 ≤ 1 < 2), which is valid.
- The magnetic quantum number [tex]\( m = 0 \)[/tex] satisfies [tex]\( -l \leq m \leq l \)[/tex] (-1 ≤ 0 ≤ 1), which is valid.
- Therefore, this set of quantum numbers is valid.

2. Set 2: [tex]\( n = 1, l = 0, m = 0 \)[/tex]
- The principal quantum number [tex]\( n = 1 \)[/tex] is a positive integer, which is valid.
- The angular momentum quantum number [tex]\( l = 0 \)[/tex] satisfies [tex]\( 0 \leq l < n \)[/tex] (0 ≤ 0 < 1), which is valid.
- The magnetic quantum number [tex]\( m = 0 \)[/tex] satisfies [tex]\( -l \leq m \leq l \)[/tex] (-0 ≤ 0 ≤ 0), which is valid.
- Therefore, this set of quantum numbers is valid.

3. Set 3: [tex]\( n = 3, l = 3, m = 3 \)[/tex]
- The principal quantum number [tex]\( n = 3 \)[/tex] is a positive integer, which is valid.
- The angular momentum quantum number [tex]\( l = 3 \)[/tex] does not satisfy [tex]\( 0 \leq l < n \)[/tex]; it should be in the range 0 to 2 (but here l = 3, which is not less than n = 3). This is invalid.
- The magnetic quantum number [tex]\( m = 3 \)[/tex] cannot be checked as the angular momentum quantum number [tex]\( l = 3 \)[/tex] itself is already invalid.

Thus, the third set [tex]\( n = 3, l = 3, m = 3 \)[/tex] is not a valid set of quantum numbers. The number 3 is the invalid set.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.