**Quantum Numbers and Electron Configuration**This section addresses how to determine the number of electrons in an atom based on specific sets of quantum numbers. Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. The relevant quantum numbers are:1. **Principal Quantum Number (n)**: Indicates the shell or energy level of an electron. Higher values of \( n \) mean higher energy levels and distance from the nucleus.2. **Angular Momentum Quantum Number (\( \ell \))**: Defines the shape of the orbital. It can range from \( 0 \) to \( n-1 \).3. **Magnetic Quantum Number (\( m_\ell \))**: Specifies the orientation of the orbital in space. It ranges from \(-\ell\) to \(+\ell\).4. **Spin Quantum Number (\( m_s \))**: Indicates the spin direction of the electron, which can be \( +\frac{1}{2} \) or \(-\frac{1}{2} \).---### Questions:1. **\( n = 2 \)** - How many electrons can exist in the second energy level?2. **\( n = 5, \ell = 2 \)** - How many electrons can occupy the 5d subshell?3. **\( n = 7, \ell = 2, m_\ell = -1 \)** - How many electrons can exist in a specific orbital of the 7d subshell with a given orientation?---By analyzing these quantum numbers, students will learn how to apply the Pauli exclusion principle and Hund's rule to determine electron configurations and understand orbital filling strategies within an atom.

The value for l when n =2 is 0 (for s) and 1(for p). So, 2 electrons in s-orbital and 6 electrons in…

Answered: How many electrons in an atom could…

How many electrons in an atom could have these sets of quantum numbers? n = 2 electrons n = 5, € = 2 electrons n = 7,€ = 2, me = -1 electrons

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

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

**Quantum Numbers and Electron Configuration**

This section addresses how to determine the number of electrons in an atom based on specific sets of quantum numbers. Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. The relevant quantum numbers are:

1. **Principal Quantum Number (n)**: Indicates the shell or energy level of an electron. Higher values of \( n \) mean higher energy levels and distance from the nucleus.

2. **Angular Momentum Quantum Number (\( \ell \))**: Defines the shape of the orbital. It can range from \( 0 \) to \( n-1 \).

3. **Magnetic Quantum Number (\( m_\ell \))**: Specifies the orientation of the orbital in space. It ranges from \(-\ell\) to \(+\ell\).

4. **Spin Quantum Number (\( m_s \))**: Indicates the spin direction of the electron, which can be \( +\frac{1}{2} \) or \(-\frac{1}{2} \).

---

### Questions:

1. **\( n = 2 \)**
- How many electrons can exist in the second energy level?

2. **\( n = 5, \ell = 2 \)**
- How many electrons can occupy the 5d subshell?

3. **\( n = 7, \ell = 2, m_\ell = -1 \)**
- How many electrons can exist in a specific orbital of the 7d subshell with a given orientation?

---

By analyzing these quantum numbers, students will learn how to apply the Pauli exclusion principle and Hund's rule to determine electron configurations and understand orbital filling strategies within an atom.

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