Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which of the following sets of quantum numbers (ordered [tex]\(n, l, m_e\)[/tex]) are possible for an electron in an atom? Check all that apply.

A. (-2, 1, 0)

B. (3, 2, -3)

C. (4, 3, 4)

D. (2, 2, 2)

E. (4, 2, -1)

F. (3, 2, 0)

G. (5, 3, -3)

Sagot :

GinnyAnswer
To determine which sets of quantum numbers are valid for an electron in an atom, we must check each set against the three primary quantum number rules:

1. Principal Quantum Number ([tex]\(n\)[/tex]): [tex]\(n\)[/tex] must be a positive integer ([tex]\(n > 0\)[/tex]).
2. Azimuthal Quantum Number ([tex]\(l\)[/tex]): [tex]\(l\)[/tex] can be any integer from 0 to [tex]\(n-1\)[/tex] ([tex]\(0 \leq l < n\)[/tex]).
3. Magnetic Quantum Number ([tex]\(m_e\)[/tex]): [tex]\(m_e\)[/tex] can be any integer ranging from [tex]\(-l\)[/tex] to [tex]\(+l\)[/tex] ([tex]\(-l \leq m_e \leq l\)[/tex]).

Let's evaluate each given set of quantum numbers one by one:

1. [tex]\((-2, 1, 0)\)[/tex]
- [tex]\(n = -2\)[/tex]: Not valid because [tex]\(n\)[/tex] must be positive.

2. [tex]\((3, 2, -3)\)[/tex]
- [tex]\(n = 3\)[/tex]: Valid.
- [tex]\(l = 2\)[/tex]: Valid because [tex]\(0 \leq 2 < 3\)[/tex].
- [tex]\(m_e = -3\)[/tex]: Not valid because [tex]\(-2 \leq m_e \leq 2\)[/tex].

3. [tex]\((4, 3, 4)\)[/tex]
- [tex]\(n = 4\)[/tex]: Valid.
- [tex]\(l = 3\)[/tex]: Valid because [tex]\(0 \leq 3 < 4\)[/tex].
- [tex]\(m_e = 4\)[/tex]: Not valid because [tex]\(-3 \leq m_e \leq 3\)[/tex].

4. [tex]\((2, 2, 2)\)[/tex]
- [tex]\(n = 2\)[/tex]: Valid.
- [tex]\(l = 2\)[/tex]: Not valid because [tex]\(l\)[/tex] must be less than [tex]\(n\)[/tex] (i.e., [tex]\(0 \leq l < 2\)[/tex]).

5. [tex]\((4, 2, -1)\)[/tex]
- [tex]\(n = 4\)[/tex]: Valid.
- [tex]\(l = 2\)[/tex]: Valid because [tex]\(0 \leq 2 < 4\)[/tex].
- [tex]\(m_e = -1\)[/tex]: Valid because [tex]\(-2 \leq m_e \leq 2\)[/tex].

6. [tex]\((3, 2, 0)\)[/tex]
- [tex]\(n = 3\)[/tex]: Valid.
- [tex]\(l = 2\)[/tex]: Valid because [tex]\(0 \leq 2 < 3\)[/tex].
- [tex]\(m_e = 0\)[/tex]: Valid because [tex]\(-2 \leq m_e \leq 2\)[/tex].

7. [tex]\((5, 3, -3)\)[/tex]
- [tex]\(n = 5\)[/tex]: Valid.
- [tex]\(l = 3\)[/tex]: Valid because [tex]\(0 \leq 3 < 5\)[/tex].
- [tex]\(m_e = -3\)[/tex]: Valid because [tex]\(-3 \leq m_e \leq 3\)[/tex].

So, the valid sets of quantum numbers are:

- [tex]\((4, 2, -1)\)[/tex]
- [tex]\((3, 2, 0)\)[/tex]
- [tex]\((5, 3, -3)\)[/tex]

These sets correctly satisfy all quantum number rules.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.