To learn the restrictions on each quantum number. Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers. Part A What is the only possible value of me for an electron in an s orbital? The principal quantum number n corresponds to the shell in which the electron is located. Thus n Express your answer numerically. can therefore be any integer. For example, an electron in the 2p subshell has a principal quantum number of n =2 because 2p is in the second shell. • View Available Hint(s) The azimuthal or angular momentum quantum number l corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and fas 3. For example, an electron in the 2p subshell has l = 1. As a rule, l can have integer values ranging from 0 to n –1. Submit Request Answer The magnetic quantum number me corresponds to the orbital in which the electron is located. Instead Part B of 2px, 2py, and 2pz, the three 2p orbitals can be labeled –1, 0, and 1, but not necessarily respectively. As a rule, me can have integer values ranging from -l to +l. What are the possible values of me for an electron in a d orbital? Express your answer numerically with sequential values separated by commas. • View Available Hint(s) The spin quantum number ms corresponds to the spin of the electron in the orbital. A value of 1/2 means an "up" spin, whereas -1/2 means a "down" spin.

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter7: Atomic Structure And Periodicity
Section: Chapter Questions
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**Learning Goal:**

To learn the restrictions on each quantum number.

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.

The *principal quantum number* \( n \) corresponds to the shell in which the electron is located. Thus \( n \) can therefore be any integer. For example, an electron in the \( 2p \) subshell has a principal quantum number of \( n = 2 \) because \( 2p \) is in the second shell.

The *azimuthal or angular momentum quantum number* \( \ell \) corresponds to the subshell in which the electron is located. \( s \) subshells are coded as 0, \( p \) subshells as 1, \( d \) as 2, and \( f \) as 3. For example, an electron in the \( 2p \) subshell has \( \ell = 1 \). As a rule, \( \ell \) can have integer values ranging from 0 to \( n - 1 \).

The *magnetic quantum number* \( m_\ell \) corresponds to the orbital in which the electron is located. Instead of \( 2p_x \), \( 2p_y \), and \( 2p_z \), the three \( 2p \) orbitals can be labeled \( -1 \), 0, and 1, but not necessarily respectively. As a rule, \( m_\ell \) can have integer values ranging from \( -\ell \) to \( +\ell \).

The *spin quantum number* \( m_s \) corresponds to the spin of the electron in the orbital. A value of \( 1/2 \) means an "up" spin, whereas \( -1/2 \) means a "down" spin.

---

**Part A**

What is the only possible value of \( m_\ell \) for an electron in an \( s \) orbital?

*Express your answer numerically.*

- [ ] View Available Hint(s)

\[ \text{Answer Box} \]

\[ \text{Submit} \quad \text{Request Answer} \]

---

**Part B**

What are the possible values of \( m_\ell \) for an electron in a \( d \) orbital?

*Express your answer numerically with sequential values separated by
Transcribed Image Text:**Learning Goal:** To learn the restrictions on each quantum number. Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers. The *principal quantum number* \( n \) corresponds to the shell in which the electron is located. Thus \( n \) can therefore be any integer. For example, an electron in the \( 2p \) subshell has a principal quantum number of \( n = 2 \) because \( 2p \) is in the second shell. The *azimuthal or angular momentum quantum number* \( \ell \) corresponds to the subshell in which the electron is located. \( s \) subshells are coded as 0, \( p \) subshells as 1, \( d \) as 2, and \( f \) as 3. For example, an electron in the \( 2p \) subshell has \( \ell = 1 \). As a rule, \( \ell \) can have integer values ranging from 0 to \( n - 1 \). The *magnetic quantum number* \( m_\ell \) corresponds to the orbital in which the electron is located. Instead of \( 2p_x \), \( 2p_y \), and \( 2p_z \), the three \( 2p \) orbitals can be labeled \( -1 \), 0, and 1, but not necessarily respectively. As a rule, \( m_\ell \) can have integer values ranging from \( -\ell \) to \( +\ell \). The *spin quantum number* \( m_s \) corresponds to the spin of the electron in the orbital. A value of \( 1/2 \) means an "up" spin, whereas \( -1/2 \) means a "down" spin. --- **Part A** What is the only possible value of \( m_\ell \) for an electron in an \( s \) orbital? *Express your answer numerically.* - [ ] View Available Hint(s) \[ \text{Answer Box} \] \[ \text{Submit} \quad \text{Request Answer} \] --- **Part B** What are the possible values of \( m_\ell \) for an electron in a \( d \) orbital? *Express your answer numerically with sequential values separated by
**Learning Goal:**

To learn the restrictions on each quantum number.

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.

- **The principal quantum number \( n \):** Corresponds to the shell in which the electron is located. Thus \( n \) can therefore be any integer. For example, an electron in the \( 2p \) subshell has a principal quantum number of \( n = 2 \) because \( 2p \) is in the second shell.

- **The azimuthal or angular momentum quantum number \( \ell \):** Corresponds to the subshell in which the electron is located. \( s \) subshells are coded as 0, \( p \) subshells as 1, \( d \) as 2, and \( f \) as 3. For example, an electron in the \( 2p \) subshell has \( \ell = 1 \). As a rule, \( \ell \) can have integer values ranging from 0 to \( n - 1 \).

- **The magnetic quantum number \( m_\ell \):** Corresponds to the orbital in which the electron is located. Instead of \( 2p_x \), \( 2p_y \), and \( 2p_z \), the three \( 2p \) orbitals can be labeled \( -1, 0, \) and 1, but not necessarily respectively. As a rule, \( m_\ell \) can have integer values ranging from \( -\ell \) to \( +\ell \).

- **The spin quantum number \( m_s \):** Corresponds to the spin of the electron in the orbital. A value of \( 1/2 \) means an "up" spin, whereas \( -1/2 \) means a "down" spin.

---

**Part C**

**Question:** Which of the following set of quantum numbers (ordered \( n, \ell, m_\ell, m_s \)) are possible for an electron in an atom? 

*Check all that apply.*

1. \(-1, 0, 0, -1/2\)
2. \(3, 2, 0, -1/2\)
3. \(3, 2, 2, -1/2\)
Transcribed Image Text:**Learning Goal:** To learn the restrictions on each quantum number. Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers. - **The principal quantum number \( n \):** Corresponds to the shell in which the electron is located. Thus \( n \) can therefore be any integer. For example, an electron in the \( 2p \) subshell has a principal quantum number of \( n = 2 \) because \( 2p \) is in the second shell. - **The azimuthal or angular momentum quantum number \( \ell \):** Corresponds to the subshell in which the electron is located. \( s \) subshells are coded as 0, \( p \) subshells as 1, \( d \) as 2, and \( f \) as 3. For example, an electron in the \( 2p \) subshell has \( \ell = 1 \). As a rule, \( \ell \) can have integer values ranging from 0 to \( n - 1 \). - **The magnetic quantum number \( m_\ell \):** Corresponds to the orbital in which the electron is located. Instead of \( 2p_x \), \( 2p_y \), and \( 2p_z \), the three \( 2p \) orbitals can be labeled \( -1, 0, \) and 1, but not necessarily respectively. As a rule, \( m_\ell \) can have integer values ranging from \( -\ell \) to \( +\ell \). - **The spin quantum number \( m_s \):** Corresponds to the spin of the electron in the orbital. A value of \( 1/2 \) means an "up" spin, whereas \( -1/2 \) means a "down" spin. --- **Part C** **Question:** Which of the following set of quantum numbers (ordered \( n, \ell, m_\ell, m_s \)) are possible for an electron in an atom? *Check all that apply.* 1. \(-1, 0, 0, -1/2\) 2. \(3, 2, 0, -1/2\) 3. \(3, 2, 2, -1/2\)
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