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

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.