# 14.1: Nuclei Have Intrinsic Spin Angular Momenta

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- 210914

The electron, as well as certain other fundamental particles, possesses an intrinsic angular momentum or *spin*, in addition to its orbital angular momentum. These two types of angular momentum are analogous to the daily and annual motions, respectively, of the Earth around the Sun. To distinguish the spin angular momentum from the orbital, we designate the quantum numbers as *s* and \( m_s \), in place of \( \ell \) and *m*. For the electron, the quantum number *s* always has the value \( \dfrac{1}{2} \), while \(m_s \) can have one of two values,\( \pm \dfrac{1}{2} \). The electron is said to be an elementary particle of spin \( \dfrac{1}{2} \). The proton and neutron also have spin \( \dfrac{1}{2} \) and belong to the classification of particles called *fermions*, which are governed by the Pauli exclusion principle. Other particles, including the photon, have integer values of spin and are classified as *bosons*. These do *not *obey the Pauli principle, so that an arbitrary number can occupy the same quantum state. A complete theory of spin requires relativistic quantum mechanics. For our purposes, it is sufficient to recognize the two possible internal states of the electron, which can be called `spin up' and `spin down.' These are designated, respectively, by \( \alpha \) and \( \beta \) as factors in the electron wavefunction. Spins play an essential role in determining the possible electronic states of atoms and molecules.