Quantum Numbers Of Ion X²⁻: A Chemistry Discussion

Oct 22, 2025 by Dimemap Team 51 views

Hey guys! Today, we're diving into a fun little problem from chemistry that involves figuring out the quantum numbers of an ion. Specifically, we need to determine the quantum numbers for the last electron of atom X, given that the ion X²⁻ has the electron configuration $1s^2 2s^2 2p^6 3s^2 3p^6$ . Sounds like a blast, right? Let's break it down step by step so we can all understand it perfectly.

Understanding the Problem

First, let's make sure we understand what the question is asking. We have an ion, $X^{2-}$ , which means that an atom X has gained two electrons. The electron configuration provided, $1s^2 2s^2 2p^6 3s^2 3p^6$ , tells us how the electrons are arranged in the ion. Our mission is to find the set of four quantum numbers ( $n$ , $l$ , $m_l$ , and $s$ ) that describe the very last electron added to form this ion. Essentially, we are working backward to understand the properties of the electron that completed the configuration.

Why is this important? Well, quantum numbers are like the electron's address. They tell us a lot about the electron's energy level, shape of its orbital, its orientation in space, and its spin. By finding these numbers, we gain a deeper understanding of the electronic structure of the atom and its chemical behavior. The specific electron configuration and quantum numbers influence how elements interact with each other, forming molecules and compounds. Understanding the quantum numbers also gives insight into the chemical properties of elements and how they might react with other elements.

Moreover, working with electron configurations and quantum numbers sharpens our understanding of atomic theory and quantum mechanics. These concepts are fundamental to understanding chemical bonding, molecular structure, and spectroscopy. This understanding has practical applications in various fields, including material science, nanotechnology, and drug discovery. The ability to accurately predict and manipulate electronic structures allows for the design of new materials with specific properties, the development of more efficient chemical processes, and the creation of new pharmaceuticals. It's a crucial skill for anyone serious about chemistry, and it's fascinating stuff!

Step-by-Step Solution

1. Identify the Last Electron

The electron configuration $1s^2 2s^2 2p^6 3s^2 3p^6$ tells us that the last electrons were added to the $3p$ subshell. Specifically, the last electron filled the $3p$ subshell. This is super important because it directly gives us the principal quantum number and the azimuthal quantum number.

2. Determine the Principal Quantum Number (n)

The principal quantum number, n, describes the energy level of the electron. In our case, the last electron is in the $3p$ subshell, so n = 3. Easy peasy! This means our electron is in the third energy level.

3. Determine the Azimuthal Quantum Number (l)

The azimuthal quantum number, l, describes the shape of the electron's orbital and ranges from 0 to n - 1. For a p subshell, l = 1. Remember that l = 0 corresponds to an s orbital, l = 1 corresponds to a p orbital, l = 2 corresponds to a d orbital, and l = 3 corresponds to an f orbital. Got it memorized?

4. Determine the Magnetic Quantum Number (ml)

The magnetic quantum number, $m_l$ , describes the orientation of the electron's orbital in space. It can take any integer value from -l to +l, including 0. Since l = 1 for a p orbital, $m_l$ can be -1, 0, or +1. To determine which one the last electron occupies, we need to consider Hund's rule, which states that electrons will individually occupy each orbital within a subshell before doubling up in any one orbital. In other words, electrons will try to maximize their spin. Given that the $3p$ subshell is completely filled ( $3p^6$ ), the last electron will be in the last available orbital, which we can assign as $m_l$ = +1. However, the question does not specify where the last electron enters. Typically, we consider the last electron to fill the last available slot. Let's consider a scenario where the electron fills the $m_l = -1$ orbital. This is equally valid without additional information.

5. Determine the Spin Quantum Number (s)

The spin quantum number, s, describes the intrinsic angular momentum of the electron, which is also quantized and referred to as spin. Electrons behave as though they are spinning, creating a magnetic moment. This spin can be either spin-up or spin-down, corresponding to $s = + ${\frac{1}{2}}$ $ or $s = - ${\frac{1}{2}}$ $, respectively. Since the $3p$ subshell is filled, the last electron must pair up with an existing electron in the $m_l = -1$ orbital. Therefore, it will have the opposite spin, $s = - ${\frac{1}{2}}$ $.

Possible Answer

Given the options and our step-by-step reasoning, the correct set of quantum numbers for the last electron of atom X is:

n = 3, l = 1, $m_l$ = -1, s = -1/2

Key Takeaways

Electron Configuration: Understanding electron configurations is crucial for determining quantum numbers.
Quantum Numbers: Knowing what each quantum number represents is essential for solving these types of problems.
Hund's Rule: Hund's rule helps determine the $m_l$ and s values, especially when dealing with partially filled subshells.
Ions: Remember that ions gain or lose electrons, affecting their electron configurations.

Practice Makes Perfect

The best way to master these concepts is through practice. Try working through similar problems with different electron configurations and ions. You can also explore online resources and textbooks for more examples and explanations. Keep at it, and you'll become a quantum number pro in no time! Understanding these concepts not only helps in acing exams but also provides a solid foundation for advanced chemistry topics. Keep exploring and enjoy the journey of learning chemistry!

So, there you have it! A comprehensive breakdown of how to find the quantum numbers for the last electron of an ion. Remember to take your time, understand each step, and don't be afraid to ask for help when you need it. Chemistry can be challenging, but it's also incredibly rewarding. Keep exploring and have fun!

I hope this helps clarify any confusion. If you have more questions or want to explore other chemistry topics, just let me know. Happy studying!