A certain orbital of the hydrogen atom has n = 4 and l = 3. (b) What are the possible values of ms for the orbital?

Verified step by step guidance

1. Step 1: Understand the quantum numbers. The principal quantum number (n) describes the energy level of the electron in the hydrogen atom. The azimuthal quantum number (l) describes the shape of the orbital. The magnetic quantum number (ml) describes the orientation of the orbital in space. The spin quantum number (ms) describes the spin of the electron.
2. Step 2: The spin quantum number (ms) has only two possible values, regardless of the values of the other quantum numbers. These values are +1/2 and -1/2.
3. Step 3: The +1/2 value represents an electron spinning in one direction (often referred to as 'spin up'), and the -1/2 value represents an electron spinning in the opposite direction (often referred to as 'spin down').
4. Step 4: Therefore, for any given orbital of the hydrogen atom, the possible values of ms are +1/2 and -1/2.

Key Concepts

Quantum Numbers

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

Principal Quantum Number (n)

The principal quantum number (n) indicates the main energy level of an electron in an atom and can take positive integer values (1, 2, 3, ...). A higher value of n corresponds to a higher energy level and a greater average distance of the electron from the nucleus. In this case, n = 4 signifies that the electron is in the fourth energy level.

Spin Quantum Number (m_s)

The spin quantum number (m_s) describes the intrinsic angular momentum or 'spin' of an electron, which can have one of two possible values: +1/2 or -1/2. This property is crucial for determining the orientation of the electron's spin and is essential for understanding electron pairing and the Pauli exclusion principle in atomic structure.