Problem 80 Which of the following sets of q... [FREE SOLUTION]

Chapter 7: Problem 80

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. \(n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}\) b. \(n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}\) c. \(n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-1\) e. \(n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}\) f. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)

Short Answer

Expert verified

Sets A, D, E, and F are not allowed due to the following reasons: a. Set A is not allowed because 鈩�=3, which is outside the allowed range (0 to n-1) for n=3. d. Set D is not allowed because m_s=-1, which is not a valid value (must be +1/2 or -1/2). e. Set E is not allowed because 鈩�=-4, which is negative and not a valid value (must be within the range 0 to n-1). f. Set F is not allowed because m_鈩�=2 is outside the allowed range of -鈩� and +鈩� for a given value of 鈩�=1.

Step by step solution

Set A: n=3, 鈩�=3, m_鈩�=0, m_s=-1/2

Since the angular momentum quantum number (鈩�) must be in the range of 0 to (n-1), and here n = 3, the allowed values for 鈩� would be 0, 1, and 2. As 鈩� = 3, this set is not allowed.

Set B: n=4, 鈩�=3, m_鈩�=2, m_s=-1/2

This set is allowed, as all the quantum numbers follow the restrictions: n = 4, 鈩� ranges from 0 to 3, m_鈩� ranges from -3 to 3, and m_s can be either 卤1/2.

Set C: n=4, 鈩�=1, m_鈩�=1, m_s=+1/2

This set is allowed, as all the quantum numbers follow the restrictions: n = 4, 鈩� ranges from 0 to 3, m_鈩� ranges from -1 to 1, and m_s can be either 卤1/2.

Set D: n=2, 鈩�=1, m_鈩�=-1, m_s=-1

In this set, the spin quantum number (m_s) is not allowed, as it must be either +1/2 or -1/2. Here it is given as -1, which is not a valid value.

Set E: n=5, 鈩�=-4, m_鈩�=2, m_s=+1/2

In this set, the angular momentum quantum number (鈩�) is not allowed, as it must be in the range of 0 to (n-1) and cannot be negative. Here it is given as -4, which is not a valid value.

Set F: n=3, 鈩�=1, m_鈩�=2, m_s=-1/2

In this set, the magnetic quantum number (m_鈩�) is not allowed, as it must be in the range of -鈩� to +鈩� for a given value of 鈩�. Here, m_鈩� = 2 is not within the range of values for 鈩� = 1 (which should be -1 to 1).

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Set A: n=3, 鈩�=3, m_鈩�=0, m_s=-1/2

Set B: n=4, 鈩�=3, m_鈩�=2, m_s=-1/2

Set C: n=4, 鈩�=1, m_鈩�=1, m_s=+1/2

Set D: n=2, 鈩�=1, m_鈩�=-1, m_s=-1

Set E: n=5, 鈩�=-4, m_鈩�=2, m_s=+1/2

Set F: n=3, 鈩�=1, m_鈩�=2, m_s=-1/2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Physical Chemistry

Ionic and Molecular Compounds

Kinetics

Chemical Analysis

Chemistry Branches

Study anywhere. Anytime. Across all devices.