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Chapter 3: Problem 26

For each of the questions, four choices have been provided. Select the correct alternative. Which of the following sets of quantum numbers is correct for an electron in \(3 \mathrm{~d}\) orbital? (a) \(3,0,0,+1 / 2\) (b) \(3,1,1,-1 / 2\) (c) \(3,2,1,+1 / 2\) (d) \(3,2,3,-1 / 2\)

Short Answer

Expert verified
Answer: The correct set of quantum numbers for an electron in a 3d orbital is (c) \(3,2,1,+1 / 2\).

Step by step solution

01

Principal Quantum Number (n)

For a 3d orbital, the principal quantum number (n) must be equal to 3.
02

Angular Momentum Quantum Number (l)

For d orbitals, the angular momentum quantum number (l) must be equal to 2.
03

Magnetic Quantum Number (m_l)

The magnetic quantum number (m_l) can have integer values ranging from -l to +l, inclusive. For d orbitals (l=2), m_l can be -2, -1, 0, 1, or 2.
04

Electron Spin Quantum Number (m_s)

The electron spin quantum number (m_s) can have two values: +1/2 and -1/2.
05

Compare and Select the Correct Set of Quantum Numbers

Compare each set of given quantum numbers to the values derived for a 3d orbital: (a) \(3,0,0,+1 / 2\) - l is incorrect (b) \(3,1,1,-1 / 2\) - l is incorrect (c) \(3,2,1,+1 / 2\) - n, l, m_l, and m_s are all within the correct range (d) \(3,2,3,-1 / 2\) - m_l is incorrect Only option (c) has the correct values for all four quantum numbers. Therefore, the correct set of quantum numbers for an electron in a 3d orbital is: (c) \(3,2,1,+1 / 2\)

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Direction for questions: State whether the following statements are true or false. Azimuthal quantum number indicates the angular momentum of an electron.
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