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 3.84QA
Interpretation Introduction

To determine:

which of the given combinations of quantum numbers are allowed

Expert Solution & Answer
Check Mark

Answer to Problem 3.84QA

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

No. Quantum Numbers Allowed
a. n=3,l=2,ml=0,ms=-12 Yes
b. n=5,l=4,ml=4,ms=+12 Yes
c. n=3,l=0,ml=1,ms=+12 No
d. n=4,l=4,ml=1,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:

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

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

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

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

2) Given Information:

No. Quantum Numbers
a. n=3,l=2,ml=0,ms=-12
b. n=5,l=4,ml=4,ms=+12
c. n=3,l=0,ml=1,ms=+12
d. n=4,l=4,ml=1,ms=-12

3) Calculations:

a) n=3,l=2,ml=0,ms=-12

For l=2, the possible ml values range from -2 to +2. Therefore, this combination is allowed.

b) n=5,l=4,ml=4,ms=+12

For l=4, the possible ml values range from -4 to +4. Therefore, this combination is allowed.

c) n=3,l=0,ml=1,ms=+12

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

d) n=4,l=4,ml=1,ms=-12

For n=4, the possible l values are 0 to 3. Therefore, this combination is not allowed.

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

No. Quantum Numbers Allowed
a. n=3,l=2,ml=0,ms=-12 Yes
b. n=5,l=4,ml=4,ms=+12 Yes
c. n=3,l=0,ml=1,ms=+12 No
d. n=4,l=4,ml=1,ms=-12 No

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Chapter 3 Solutions

Chemistry: An Atoms-Focused Approach

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