Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Chapter 7, Problem 87E

Give the maximum number of electrons in an atom that can have these quantum numbers:

a. n = 4

b. n = 5, ml = + l

c. n = 5,ms = + 1 2

d. n = 3, l = 2

e. n = 2, l = 1

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The maximum number of electrons for the given quantum numbers to be predicted.

Concept Introduction:

In an electronic configuration, each subshell can only have a definite number of orbitals. In s subshell, the number of orbitals is 1; in subshell p the number of orbitals is 3 , in d subshell the number of orbitals is 5 , in the f subshell the number orbitals is 7 and in subshell g the number of orbitals is 9 . The maximum number of electrons present in each orbital is 2.

To determine: The maximum number of electrons present in an atom having quantum number n=4 .

Answer to Problem 87E

Answer

The maximum number of electrons present in an atom with quantum number n=4 are 32_ .

Explanation of Solution

The maximum number of electrons present in an atom with quantum number n is 2n2

Where,

  • n is the principal quantum number

For quantum number n=4 , the sub-shells possible are,

n=4s,4p,4d,4f

Number of orbitals possible in subshell 4s is 1 .

Numbers of orbitals possible in subshell 4p are 3 .

Numbers of orbitals possible in subshell 4d are 5 .

Numbers of orbitals possible in subshell 4f are 7 .

Therefore, the total number of orbitals possible for quantum number, n=4 is

1+3+5+7=16

The maximum number of electrons present in each orbital is 2 .

Therefore, for n=4 , the maximum number of electrons present is 16×2=32_ .

Conclusion

The maximum number of electrons present in an atom with quantum number, n=4 are 32_ .

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The maximum number of electrons for the given quantum numbers to be predicted.

Concept Introduction:

In an electronic configuration, each subshell can only have a definite number of orbitals. In s subshell, the number of orbitals is 1; in subshell p the number of orbitals is 3 , in d subshell the number of orbitals is 5 , in the f subshell the number orbitals is 7 and in subshell g the number of orbitals is 9 . The maximum number of electrons present in each orbital is 2.

To determine: The maximum number of electrons present in an atom having quantum number n=5andml=+1 .

Answer to Problem 87E

Answer

The maximum number of electrons present in an atom with quantum number n=5andml=+1 are 8_ .

Explanation of Solution

The number of subshell having the same quantum number n=5andml=+1 ,

Principal quantum number (n) Orbital quantum number (l=0to(n1)) Magnetic quantum number (ml=lto+l)
5 0 0
5 1 1,0+1
5 2 2,1,0,+1,+2
5 3 3,2,1,0,+1,+2,+3
5 4 4,3,2,1,0,+1,+2,+3,+4

From the above table it can be stated that there are 4 orbitals for which the value of quantum number, n=5andml=+1 .

In each orbital the maximum number of electrons that can be present is 2 .

Therefore, the total number of electrons present in the orbital having quantum number n=5andml=+1 is 2×4=8_ .

Conclusion

The maximum number of electrons present in an atom with quantum number n=5andml=+1 is 8_ .

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The maximum number of electrons for the given quantum numbers to be predicted.

Concept Introduction:

In an electronic configuration, each subshell can only have a definite number of orbitals. In s subshell, the number of orbitals is 1; in subshell p the number of orbitals is 3 , in d subshell the number of orbitals is 5 , in the f subshell the number orbitals is 7 and in subshell g the number of orbitals is 9 . The maximum number of electrons present in each orbital is 2.

To determine: The maximum number of electrons present in an atom having quantum number n=5andms=+12 .

Answer to Problem 87E

Answer

The maximum number of electrons present in an atom with quantum number n=5andms=+12 is 25_ .

Explanation of Solution

The number of subshell having the same quantum number n=5andml=+1 ,

Principal quantum number (n) Orbital quantum number (l=0to(n1)) Magnetic quantum number (ml=lto+l)
5 0 0
5 1 1,0+1
5 2 2,1,0,+1,+2
5 3 3,2,1,0,+1,+2,+3
5 4 4,3,2,1,0,+1,+2,+3,+4

The total number of orbitals for quantum number n=5 is,

1+3+5+7+9=25

In each orbital, the maximum number of electrons that can be present is 2 ; one of the electron will revolve positively and have value of spin quantum number, ms=+12 while the other electron will have the spin quantum number, ms=12 . Therefore, there are total 25_ orbitals for which the value of quantum number n=5andms=+12 .

Conclusion

The possible number of electrons that can have the value of quantum number n=5andms=+12 is 25_ .

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The maximum number of electrons for the given quantum numbers to be predicted.

Concept Introduction:

In an electronic configuration, each subshell can only have a definite number of orbitals. In s subshell, the number of orbitals is 1; in subshell p the number of orbitals is 3 , in d subshell the number of orbitals is 5 , in the f subshell the number orbitals is 7 and in subshell g the number of orbitals is 9 . The maximum number of electrons present in each orbital is 2.

To determine: The maximum number of electrons present in an atom having quantum number n=3andl=2 .

Answer to Problem 87E

Answer

The maximum number of electrons present in an atom with quantum number n=3andl=2 is 10_ .

Explanation of Solution

The number of subshell having the same quantum number n=3andl=2 ,

Principal quantum number (n) Orbital quantum number (l=0to(n1)) Magnetic quantum number (ml=lto+l)
3 0 0
3 1 1,0+1
3 2 2,1,0,+1,+2
3 3 3,2,1,0,+1,+2,+3

The total number of orbitals for quantum number n=3andl=2 is 5 .

In each orbital, the maximum number of electrons that can be present is 2 .

Therefore maximum number of electron for which the value of quantum number is n=3,l=2 is 5×2=10_ .

Conclusion

The possible number of electrons that can have the value of quantum number n=3,l=2 is 10_ .

(e)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The maximum number of electrons for the given quantum numbers to be predicted.

Concept Introduction:

In an electronic configuration, each subshell can only have a definite number of orbitals. In s subshell, the number of orbitals is 1; in subshell p the number of orbitals is 3 , in d subshell the number of orbitals is 5 , in the f subshell the number orbitals is 7 and in subshell g the number of orbitals is 9 . The maximum number of electrons present in each orbital is 2.

To determine: The maximum number of electrons present in an atom having quantum number n=2andl=1 .

Answer to Problem 87E

Answer

The maximum number of electrons present in an atom with quantum number n=2andl=1 is 6_ .

Explanation of Solution

The number of subshell having the same quantum number n=2andl=1 ,

Principal quantum number (n) Orbital quantum number (l=0to(n1)) Magnetic quantum number (ml=lto+l)
2 0 0
2 1 1,0+1
2 2 2,1,0,+1,+2

The total number of orbital for quantum number n=2,l=1 is 3 .

In each orbital, the maximum number of electrons that can be present is 2 .

Therefore, maximum number of electrons for which the value of quantum number is n=2andl=1 is 3×2=6_ .

Conclusion

The possible number of electrons that can have the value of quantum number n=2andl=1 is 6_ .

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Chapter 7 Solutions

Chemistry

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