What are the possible values of m_l for each value of l? b. 1

Verified step by step guidance

1. Identify the quantum number \( l \) given in the problem. Here, \( l = 1 \).
2. Recall that the magnetic quantum number \( m_l \) can take integer values ranging from \( -l \) to \( +l \), inclusive.
3. For \( l = 1 \), determine the range of \( m_l \) values. This means \( m_l \) can be \( -1, 0, \) or \( +1 \).
4. List the possible values of \( m_l \) for \( l = 1 \): \( m_l = -1, 0, +1 \).
5. Understand that these values of \( m_l \) correspond to the different orientations of an orbital in a magnetic field.

Key Concepts

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms). Each quantum number provides specific information about the electron's energy level, shape, orientation, and spin.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) determines the shape of an electron's orbital and can take on integer values from 0 to n-1, where n is the principal quantum number. For example, if l = 1, it corresponds to a p orbital, which has a specific shape and energy level. The value of l is crucial for understanding the types of orbitals and their properties.

Magnetic Quantum Number (ml)

The magnetic quantum number (ml) specifies the orientation of an orbital in space and can take on integer values ranging from -l to +l, including zero. For instance, if l = 1, the possible values of ml are -1, 0, and +1, corresponding to the three p orbitals. This concept is essential for visualizing how orbitals are arranged in a magnetic field and their spatial distribution.