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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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Most popular questions from this chapter

Match the entries given in column A with appropriate ones from column B. $$ \begin{array}{|l|ll|l|l|} {\text { Column A }} & {\text { Column B }} \\ \hline \text { A. } & \text { Be } & (\cdot) & \text { a. } & {[\mathrm{He}] 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6}} \\ \hline \text { B. } & \mathrm{Ne} & (\cdot) & \text { b. } & {[\mathrm{He}] 2 \mathrm{~s}^{2}} \\ \hline \text { C. } & \text { Si } & (\cdot) & \text { c. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{3}} \\ \hline \text { D. } & \mathrm{P} & (\cdot) & \text { d. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{5}} \\ \hline \text { E. } & \text { Cl } & (\cdot) & \text { e. } & {[\mathrm{Ne}] 3 s^{2} 3 \mathrm{p}^{2}} \\ \hline \end{array} $$

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Direction for questions: State whether the following statements are true or false. Pairing of electrons in degenerate orbitals takes place only when the degenerate orbitals are filled with one electron each.

For each of the questions, four choices have been provided. Select the correct alternative. The statements given below are the postulates of various atomic models. Arrange them in their chronological order. (1) Fine structure is due to the presence of subshells in the main energy level. (2) The size of an atom is much larger than the size of its nucleus. (3) As long as the electron is present in a particular orbit, its energy remains constant. (4) Negatively charged particles are uniformly spread in the lump of positive charge. (a) \(4,3,2,1\) (b) \(2,3,4,1\) (c) \(4,2,3,1\) (d) \(3,4,2,1\)
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