A certain orbital of the hydrogen atom has n = 4 and l = 2. b. What are the possible values of ms for the orbital?

Verified step by step guidance

1. Identify the quantum numbers involved: n (principal quantum number), l (azimuthal quantum number), m_l (magnetic quantum number), and m_s (spin quantum number).
2. Understand that the spin quantum number, m_s, describes the intrinsic angular momentum (or spin) of an electron within an orbital.
3. Recall that the possible values for m_s are always +\(\frac{1}{2}\) and -\(\frac{1}{2}\), regardless of the values of n, l, or m_l.
4. Note that the problem specifies an orbital with n = 4 and l = 2, but these do not affect the possible values of m_s.
5. Conclude that the possible values of m_s for any electron in any orbital are +\(\frac{1}{2}\) and -\(\frac{1}{2}\).

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 principal quantum number (n) indicates the energy level, while the azimuthal quantum number (l) defines the shape of the orbital. For each value of l, there are specific allowed values for the magnetic quantum number (m_l) and the spin quantum number (m_s).

Spin Quantum Number (m_s)

The spin quantum number (m_s) describes the intrinsic angular momentum or 'spin' of an electron within an orbital. It can take on one of two values: +1/2 or -1/2, representing the two possible orientations of the electron's spin. This concept is crucial for understanding the behavior of electrons in magnetic fields and the overall electron configuration of atoms.

Orbital Types and Their Characteristics

Orbitals are regions in an atom where there is a high probability of finding electrons. The type of orbital is determined by the azimuthal quantum number (l), where l = 0 corresponds to s orbitals, l = 1 to p orbitals, l = 2 to d orbitals, and l = 3 to f orbitals. In this case, with n = 4 and l = 2, we are dealing with a 4d orbital, which can hold a maximum of 10 electrons, each with a unique set of quantum numbers.