Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29, Problem 1OQ
To determine

The number of electrons can be placed in the n=3 energy level in a hydrogen atom.

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Answer to Problem 1OQ

The number of electrons can be placed in the n=3 energy level in a hydrogen atom is 18_ .

Explanation of Solution

In this case, the principal quantum number, n=3 .

Write the expression for the orbital quantum number,

    l=n1        (I)

Here, l is the orbital quantum number and n is the principal quantum number.

Write the expression for the orbital magnetic quantum number,

    ml=2l+1        (II)

Here, ml is the orbital magnetic quantum number.

In this case, there are 2 is the possible spin orientations for each value of orbital magnetic quantum number.

    ms=±12        (III)

Here, ms is the spin orientation for each value of orbital magnetic quantum number.

Write the expression for the total possible values for each value of the orbital quantum number,

    T=2(2l+1)        (IV)

Here, T is the grand total possible value for each value of the orbital quantum number.

Write the expression for the grand total of n=3 states,

    T=T1+T2+T3        (V)

T1,T2&T3 are the possible states.

Conclusion:

Substitute 3 for n in (I),

    l=31=2

So, the possible values of orbital magnetic quantum number, l=0,1,2.

Substitute 3 for n and 0 for l in (IV),

    T1=2[2(0)+1]=2

Substitute 3 for n and 1 for l in (IV),

    T2=2[2(1)+1]=2[3]=6

Substitute 3 for n and 2 for l in (IV),

    T1=2[2(2)+1]=2[5]=10

Substitute 2 for T1 , 6 for T2 and 10 for T3 in (V),

    T=2+6+10=18

Thus, the number of states are 3s,3p&3d .

Therefore, the number of electrons can be placed in the n=3 energy level in a hydrogen atom is 18_.

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Principles of Physics: A Calculus-Based Text

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