The spin quantum number m_s describes the quantum state of an electron in an orbital with respect to its angular momentum. According to the Pauli exclusion principle, what are the values of m_s for each of the electrons in the 4s orbital of a calcium atom?

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11ecba2d_124c_55e1_a3bf_8d6a2826e470_MD0008_00 The quantum state of all electrons around an atom can be described using four quantum numbers (n, ℓ, m_ℓ, m_s): The principal quantum number n describes the main energy level (shell) of the electron and its most probable distance from the nucleus (n = 1, 2, 3, 4…). The orbital angular momentum quantum number ℓ corresponds to the subshell type (s, p, d, f) and the corresponding shape of the orbital occupied by the electron, where ℓ = 0, 1, 2, 3, 4, …, (n − 1). The magnetic quantum number m_ℓ determines the number of orbitals of a given type and their orientations within a sublevel. For a given orbital, the values of m_ℓ include all integers ranging from −ℓ to +ℓ. The electron spin quantum number m_s describes the angular momentum of an electron, which is a vector quantity with a magnitude of ½ and a direction that is either spin up (positive) or spin down (negative). The Pauli exclusion principle states that each orbital subshell can hold a maximum of two electrons, but two electrons in the same orbital must have opposite spins. Therefore, the two electrons in the 4s orbital of a calcium atom must have opposite spins of +½ and −½. (Choices A and C) Matching signs (+ or −) indicate matching electron spin orientations, and two electrons in the same orbital cannot have the same spin. (Choice D) The 4s orbital holds only two (not three) electrons, so only two values of m_s would be assigned (one for each electron). Educational objective: According to the Pauli exclusion principle, each orbital within a subshell can hold a maximum of two electrons, but two electrons in the same orbital must have opposite spins. Electron spin is a vector quantity with a magnitude of ½ and a direction that is either spin up (positive) or spin down (negative).

The Spin Quantum Number Ms Describes the Quantum State of an Electron

The Spin Quantum Number M_s Describes the Quantum State of an Electron