Chemistry: An Atoms-Focused Approach (Second Edition)
Chemistry: An Atoms-Focused Approach (Second Edition)
2nd Edition
ISBN: 9780393614053
Author: Thomas R. Gilbert, Rein V. Kirss, Stacey Lowery Bretz, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 3, Problem 3.86QA
Interpretation Introduction

To determine:

which of the given combinations of quantum numbers are allowed

Expert Solution & Answer
Check Mark

Answer to Problem 3.86QA

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 (Second Edition)

Ch. 3 - Prob. 3.11VPCh. 3 - Prob. 3.12VPCh. 3 - Prob. 3.13QACh. 3 - Prob. 3.14QACh. 3 - Prob. 3.15QACh. 3 - Prob. 3.16QACh. 3 - Prob. 3.17QACh. 3 - Prob. 3.18QACh. 3 - Prob. 3.19QACh. 3 - Prob. 3.20QACh. 3 - Prob. 3.21QACh. 3 - Prob. 3.22QACh. 3 - Prob. 3.23QACh. 3 - Prob. 3.24QACh. 3 - Prob. 3.25QACh. 3 - Prob. 3.26QACh. 3 - Prob. 3.27QACh. 3 - Prob. 3.28QACh. 3 - Prob. 3.29QACh. 3 - Prob. 3.30QACh. 3 - Prob. 3.31QACh. 3 - Prob. 3.32QACh. 3 - Prob. 3.33QACh. 3 - Prob. 3.34QACh. 3 - Prob. 3.35QACh. 3 - Prob. 3.36QACh. 3 - Prob. 3.37QACh. 3 - Prob. 3.38QACh. 3 - Prob. 3.39QACh. 3 - Prob. 3.40QACh. 3 - Prob. 3.41QACh. 3 - Prob. 3.42QACh. 3 - Prob. 3.43QACh. 3 - Prob. 3.44QACh. 3 - Prob. 3.45QACh. 3 - Prob. 3.46QACh. 3 - Prob. 3.47QACh. 3 - Prob. 3.48QACh. 3 - Prob. 3.49QACh. 3 - Prob. 3.50QACh. 3 - Prob. 3.51QACh. 3 - Prob. 3.52QACh. 3 - Prob. 3.53QACh. 3 - Prob. 3.54QACh. 3 - Prob. 3.55QACh. 3 - Prob. 3.56QACh. 3 - Prob. 3.57QACh. 3 - Prob. 3.58QACh. 3 - Prob. 3.59QACh. 3 - Prob. 3.60QACh. 3 - Prob. 3.61QACh. 3 - Prob. 3.62QACh. 3 - Prob. 3.63QACh. 3 - Prob. 3.64QACh. 3 - Prob. 3.65QACh. 3 - Prob. 3.66QACh. 3 - Prob. 3.67QACh. 3 - Prob. 3.68QACh. 3 - Prob. 3.69QACh. 3 - Prob. 3.70QACh. 3 - Prob. 3.71QACh. 3 - Prob. 3.72QACh. 3 - Prob. 3.73QACh. 3 - Prob. 3.74QACh. 3 - Prob. 3.75QACh. 3 - Prob. 3.76QACh. 3 - Prob. 3.77QACh. 3 - Prob. 3.78QACh. 3 - Prob. 3.79QACh. 3 - Prob. 3.80QACh. 3 - Prob. 3.81QACh. 3 - Prob. 3.82QACh. 3 - Prob. 3.83QACh. 3 - Prob. 3.84QACh. 3 - Prob. 3.85QACh. 3 - Prob. 3.86QACh. 3 - Prob. 3.87QACh. 3 - Prob. 3.88QACh. 3 - Prob. 3.89QACh. 3 - Prob. 3.90QACh. 3 - Prob. 3.91QACh. 3 - Prob. 3.92QACh. 3 - Prob. 3.93QACh. 3 - Prob. 3.94QACh. 3 - Prob. 3.95QACh. 3 - Prob. 3.96QACh. 3 - Prob. 3.97QACh. 3 - Prob. 3.98QACh. 3 - Prob. 3.99QACh. 3 - Prob. 3.100QACh. 3 - Prob. 3.101QACh. 3 - Prob. 3.102QACh. 3 - Prob. 3.103QACh. 3 - Prob. 3.104QACh. 3 - Prob. 3.105QACh. 3 - Prob. 3.106QACh. 3 - Prob. 3.107QACh. 3 - Prob. 3.108QACh. 3 - Prob. 3.109QACh. 3 - Prob. 3.110QACh. 3 - Prob. 3.111QACh. 3 - Prob. 3.112QACh. 3 - Prob. 3.113QACh. 3 - Prob. 3.114QACh. 3 - Prob. 3.115QACh. 3 - Prob. 3.116QACh. 3 - Prob. 3.117QACh. 3 - Prob. 3.118QACh. 3 - Prob. 3.119QACh. 3 - Prob. 3.120QACh. 3 - Prob. 3.121QACh. 3 - Prob. 3.122QACh. 3 - Prob. 3.123QACh. 3 - Prob. 3.124QACh. 3 - Prob. 3.125QACh. 3 - Prob. 3.126QACh. 3 - Prob. 3.127QACh. 3 - Prob. 3.128QACh. 3 - Prob. 3.129QACh. 3 - Prob. 3.130QACh. 3 - Prob. 3.131QACh. 3 - Prob. 3.132QACh. 3 - Prob. 3.133QACh. 3 - Prob. 3.134QA
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