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Chapter 6: Problem 72

What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) \(n=3, m_{l}=-2 ;(\mathbf{b}) n=4, l=3 ;(\mathbf{c}) n=5, l=3, m_{l}=2\) (d) \(n=4, l=1, m_{l}=0\)

Short Answer

Expert verified
\(a) 2 \ electrons; \ b) 14 \ electrons; \ c) 2 \ electrons; \ d) 2 \ electrons\)

Step by step solution

01

Determine the l value

Knowing the relation between m_l and l (that m_l varies between -l and l), we could find the possible values of l for m_l = -2. Since m_l = -2, l can be 2 (as m_l varies from -2 to +2).
02

Determine number of electrons

Considering the given principal quantum number n=3 and l=2, there is only one set of quantum numbers that satisfy the condition. There are 2 possible spin orientations (m_s) for this m_l value, so a maximum of 2 electrons can have these quantum numbers. #a) Answer: 2 electrons# #b) n=4, l=3#
03

Determine m_l values

Knowing the relationship between l and m_l (-l to +l), we could find the possible values of m_l for l = 3. The m_l values are -3, -2, -1, 0, 1, 2, and 3.
04

Determine number of electrons

Considering the given principal quantum number n=4 and l=3, there are 7 possible m_l values. For each m_l value, there are 2 possible spin orientations (m_s), resulting in a maximum of 14 electrons that can have these quantum numbers. #b) Answer: 14 electrons# #c) n=5, l=3, m_l=2#
05

Determine number of electrons

In this case, all quantum numbers are given, except for the spin quantum number (m_s). Since there are 2 possible spin orientations, a maximum of 2 electrons can have these quantum numbers. #c) Answer: 2 electrons# #d) n=4, l=1, m_l=0#
06

Determine number of electrons

All quantum numbers are given, except for the spin quantum number (m_s). Since there are 2 possible spin orientations, a maximum of 2 electrons can have these quantum numbers. #d) Answer: 2 electrons#

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