Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 3, Problem 3.83QA
Interpretation Introduction

To determine:

Which of the given combinations of quantum numbers is allowed

Expert Solution & Answer
Check Mark

Answer to Problem 3.83QA

Solution:

The combinations of quantum numbers that are allowed are as follows:

No. Quantum Numbers Allowed
a. n=1,l=1,ml=0,ms=+12 Yes
b. n=3,l=0,ml=0,ms=-12 Yes
c. n=1,l=0,ml=1,ms=-12 No
d. n=2,l=1,ml=2,ms=+12 No

Explanation of Solution

1) Concept:

Each orbital can contain a maximum of 2 electrons. The number of orbitals for a given set of numbers can be calculated using the following rules.

a. For a given value of ms, there can be only one electron for fixed values of n, l, and ml.

b. A given value of ml corresponds to a single orbital.

c. For a given value of l, (2l+1) values of m are possible, ranging from +l to -l.

d. For a given value of n, (n-1) values of l are possible.

2) Given:

No. Quantum Numbers
a. n=1,l=1,ml=0,ms=+12
b. n=3,l=0,ml=0,ms=-12
c. n=1,l=0,ml=1,ms=-12
d. n=2,l=1,ml=2,ms=+12

3) Calculations:

a. n=1,l=1,ml=0,ms=+12

For l=1, the possible ml values range from -1 to +1. Therefore, this combination is allowed.

b. n=3,l=0,ml=0,ms=-12

For l=0, the only possible ml value is 0. Therefore, this combination is allowed.

c. n=1,l=0,ml=1,ms=-12

For l=0, the only possible ml value is 0. Therefore, this combination is not allowed.

d. n=2,l=1,ml=2,ms=+12

For l=1, the possible ml values range from -1 to +1. Therefore, this combination is not allowed.

Conclusion:

The combinations of quantum numbers that are allowed are as follows:

No. Quantum Numbers Allowed
a. n=1,l=1,ml=0,ms=+12 Yes
b. n=3,l=0,ml=0,ms=-12 Yes
c. n=1,l=0,ml=1,ms=-12 No
d. n=2,l=1,ml=2,ms=+12 No

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Chapter 3 Solutions

Chemistry: An Atoms-Focused Approach

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