BILANGAN KUANTUM

Introduction

This tutorial aims to help you understand quantum numbers based on quantum mechanics theory. By grasping the concepts of electron configuration using the Aufbau principle, you can determine the quantum numbers of the last and outermost electrons. The tutorial includes examples and practice questions to enhance your understanding. It is recommended to review previous material on electron configuration for a better grasp of these concepts.

Step 1: Understand Quantum Numbers

Quantum numbers describe the properties of electrons in an atom. There are four main types of quantum numbers:

1. Principal Quantum Number (n)

   • Indicates the energy level of an electron.
   • Values: n = 1, 2, 3, ...

2. Azimuthal Quantum Number (l)

   • Relates to the shape of the orbital.
   • Values: l = 0 (s), 1 (p), 2 (d), 3 (f)

3. Magnetic Quantum Number (m_l)

   • Specifies the orientation of the orbital.
   • Values range from -l to +l.

4. Spin Quantum Number (m_s)

   • Describes the spin of the electron.
   • Values: +1/2 or -1/2

Practical Tip

Familiarize yourself with the significance of each quantum number and how they relate to electron configurations.

Step 2: Apply the Aufbau Principle

The Aufbau principle states that electrons occupy the lowest energy orbitals first before moving to higher ones. Use this principle to determine the electron configuration of an atom.

1. Start filling orbitals from the lowest energy level (1s) to the highest.
2. Follow the order of orbital filling:
   • 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

Example

For carbon (C), the electron configuration is:

• 1s² 2s² 2p²

From this configuration, you can derive:

• Last electron quantum numbers: n=2, l=1, m_l=0, m_s=+1/2 (for one of the 2p electrons)

Step 3: Determine Quantum Numbers of Outermost Electrons

Once you have the electron configuration, identify the outermost electrons to determine their quantum numbers.

1. Look at the highest energy level that contains electrons.
2. Identify the corresponding quantum numbers for each outermost electron.

Example

For oxygen (O), with an electron configuration of:

• 1s² 2s² 2p⁴
• The outermost electrons are in the 2p orbital.

The quantum numbers for the outermost electrons would be:

• n=2, l=1, m_l=-1, m_s=+1/2 (for one of the 2p electrons)
• Repeat for the other three outermost electrons.

Step 4: Practice with Example Problems

To solidify your understanding, work through example problems that require you to find the quantum numbers based on given electron configurations.

Common Pitfalls

• Forgetting to follow the correct order of orbital filling.
• Mixing up orbital shapes and their corresponding quantum numbers.
• Not paying attention to the spin of electrons in the same orbital.

Conclusion

Understanding quantum numbers is essential for studying atomic structure and electron configurations. By applying the Aufbau principle and practicing with examples, you'll become proficient in determining quantum numbers for various elements. For further learning, review the electron configuration video linked in the introduction and continue practicing with additional exercises.