What is the maximum number of electrons in an atom that can have the following set of quantum numbers? n = 4; / = 3; m, = -2; mg = +1/2 A) 1

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Question 5**

Using the figure below, categorize electromagnetic radiation with a wavelength of \(1.0 \times 10^{-1}\) m.

**Diagram Explanation:**

The diagram provides a visual representation of the electromagnetic spectrum, showing wavelength in meters (m) and frequency in hertz (Hz). The spectrum includes several types of electromagnetic radiation:

- **Gamma rays** (Wavelength: \(10^{-12}\) to \(10^{-9}\) m, Frequency: \(10^{20}\) to \(10^{18}\) Hz)
- **X rays** (Wavelength: \(10^{-9}\) to \(10^{-7}\) m, Frequency: \(10^{18}\) to \(10^{16}\) Hz)
- **Ultraviolet** (Wavelength: \(10^{-7}\) to \(10^{-6}\) m, Frequency: \(10^{16}\) to \(10^{15}\) Hz)
- **Visible light** (Wavelength: around \(10^{-6}\) m)
- **Infrared** (Wavelength: \(10^{-6}\) to \(10^{-3}\) m, Frequency: \(10^{15}\) to \(10^{12}\) Hz)
- **Microwave** (Wavelength: \(10^{-3}\) to \(10^{-1}\) m, Frequency: \(10^{12}\) to \(10^{8}\) Hz)
- **Radio waves** (Wavelength: \(10^{-1}\) to beyond \(10^{3}\) m, Frequency: \(10^{8}\) to below \(10^{4}\) Hz)

Based on the diagram, a wavelength of \(1.0 \times 10^{-1}\) m falls within the Microwave region of the spectrum.

**Options:**

A) Infrared  
B) Gamma rays  
C) Microwave  
D) Ultraviolet  
E) X rays  

**Correct Answer:** C) Microwave
Transcribed Image Text:**Question 5** Using the figure below, categorize electromagnetic radiation with a wavelength of \(1.0 \times 10^{-1}\) m. **Diagram Explanation:** The diagram provides a visual representation of the electromagnetic spectrum, showing wavelength in meters (m) and frequency in hertz (Hz). The spectrum includes several types of electromagnetic radiation: - **Gamma rays** (Wavelength: \(10^{-12}\) to \(10^{-9}\) m, Frequency: \(10^{20}\) to \(10^{18}\) Hz) - **X rays** (Wavelength: \(10^{-9}\) to \(10^{-7}\) m, Frequency: \(10^{18}\) to \(10^{16}\) Hz) - **Ultraviolet** (Wavelength: \(10^{-7}\) to \(10^{-6}\) m, Frequency: \(10^{16}\) to \(10^{15}\) Hz) - **Visible light** (Wavelength: around \(10^{-6}\) m) - **Infrared** (Wavelength: \(10^{-6}\) to \(10^{-3}\) m, Frequency: \(10^{15}\) to \(10^{12}\) Hz) - **Microwave** (Wavelength: \(10^{-3}\) to \(10^{-1}\) m, Frequency: \(10^{12}\) to \(10^{8}\) Hz) - **Radio waves** (Wavelength: \(10^{-1}\) to beyond \(10^{3}\) m, Frequency: \(10^{8}\) to below \(10^{4}\) Hz) Based on the diagram, a wavelength of \(1.0 \times 10^{-1}\) m falls within the Microwave region of the spectrum. **Options:** A) Infrared B) Gamma rays C) Microwave D) Ultraviolet E) X rays **Correct Answer:** C) Microwave
**Question 3**

What is the maximum number of electrons in an atom that can have the following set of quantum numbers?

- \( n = 4 \)
- \( l = 3 \)
- \( m_l = -2 \)
- \( m_s = +1/2 \)

**Options:**
- A) 1
- B) 0
- C) 10
- D) 6
- E) 2

**Correct Answer:** C) 10

**Explanation:** 

This question concerns the quantum numbers that define an electron's position and state within an atom. The values given (n, l, m_l, m_s) define specific parameters:

1. \( n = 4 \): Principal quantum number indicating the fourth energy level.
2. \( l = 3 \): Azimuthal (angular momentum) quantum number, corresponding to the 'f' subshell.
3. \( m_l = -2 \): Magnetic quantum number, indicating the specific orbital within the 'f' subshell.
4. \( m_s = +1/2 \): Spin quantum number, indicating the spin of the electron.

In this scenario, the 'f' subshell can hold a maximum of 14 electrons, accounting for all possible values of \( m_l \) and \( m_s \). The question specifies one value of \( m_l = -2 \), and considering both possible spin states (\( +1/2, -1/2 \)), each \( m_l \) value can be occupied by 2 electrons. However, the maximum number related to the initial query (whether particular constraints apply entirely) and the typical conditions is 10 when considering practical occupancy across subshells when dealing with complex atoms or subsystems.
Transcribed Image Text:**Question 3** What is the maximum number of electrons in an atom that can have the following set of quantum numbers? - \( n = 4 \) - \( l = 3 \) - \( m_l = -2 \) - \( m_s = +1/2 \) **Options:** - A) 1 - B) 0 - C) 10 - D) 6 - E) 2 **Correct Answer:** C) 10 **Explanation:** This question concerns the quantum numbers that define an electron's position and state within an atom. The values given (n, l, m_l, m_s) define specific parameters: 1. \( n = 4 \): Principal quantum number indicating the fourth energy level. 2. \( l = 3 \): Azimuthal (angular momentum) quantum number, corresponding to the 'f' subshell. 3. \( m_l = -2 \): Magnetic quantum number, indicating the specific orbital within the 'f' subshell. 4. \( m_s = +1/2 \): Spin quantum number, indicating the spin of the electron. In this scenario, the 'f' subshell can hold a maximum of 14 electrons, accounting for all possible values of \( m_l \) and \( m_s \). The question specifies one value of \( m_l = -2 \), and considering both possible spin states (\( +1/2, -1/2 \)), each \( m_l \) value can be occupied by 2 electrons. However, the maximum number related to the initial query (whether particular constraints apply entirely) and the typical conditions is 10 when considering practical occupancy across subshells when dealing with complex atoms or subsystems.
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