Problem 75 - Chemistry: An Atoms-Focused Approach

Question

How many quantum numbers are needed to identify an orbital?

Step-by-Step Solution

Answer

Answer: To identify an orbital, 3 quantum numbers are needed.

Step 1: Understand the concept of quantum numbers

Quantum numbers are a set of numerical values that describe the properties of an electron in an atom. They are used to specify the energy, size, shape, and orientation of orbitals around the nucleus of an atom.

Step 2: List down the different quantum numbers

There are four fundamental quantum numbers: 1. Principal quantum number (n) 2. Azimuthal quantum number (l) 3. Magnetic quantum number (m_l) 4. Spin quantum number (m_s)

Step 3: Identify the quantum numbers needed to specify an orbital

For identifying an orbital, we need to consider the first three quantum numbers (n, l, and m_l) as these three quantum numbers are specifically related to the orbitals around the nucleus. 1. Principal quantum number (n) determines the size and energy level of the orbital. 2. Azimuthal quantum number (l) defines the shape of the orbital. 3. Magnetic quantum number (m_l) specifies the orientation of the orbital in space.

Step 4: Count the required quantum numbers

We concluded that only the first three quantum numbers (n, l, and m_l) are required to identify an orbital. Answer: To identify an orbital, 3 quantum numbers are needed.