Electrons are not literally spinning balls of charge, but they do have intrinsic angular momentum. This spin rotation property is one of the weirdest but most important features of the quantum theory of fundamental particles.

Angular momentum is inertia of rotation motion. Linear momentum is inertia of translation motion. The big difference is that the type of motion which is related to each momentum is different. It is important to consider the place where the force related to rotation applies, which is appears as ‘r’ in the formula.

Because electrons of the same spin cancel each other out, the one unpaired electron in the atom will determine the spin. Electron’s hypothetical surface would have to be moving faster than the speed of light for it to rotate quickly enough to produce the observed angular momentum.

Quantum mechanically, the electron in the ground state (n=1) is not orbiting the nucleus; such an electron has zero angular momentum and its energy is less than that of any electron having non-zero angular momentum. There are example where the ground state is different from zero.

Much to their surprise, however, the two physicists found that electrons themselves act as if they are spinning very rapidly, producing tiny magnetic fields independent of those from their orbital motions. Soon the terminology ‘spin’ was used to describe this apparent rotation of subatomic particles.

A rotation of say 90° along the x-axis then gives an electron with only 50% chance of being up along z, if that property then gets measured. So obviously the electron changes under rotation. In other words, the 360° rotation changes the sign of the wave pattern, indicating that the particle has half-integral spin.

Although electron spin generates magnetic momentum, the opposite spins of the two electrons in the same orbital cancel out their magnetic momentum with no residual magnetic momentum. Atoms with unpaired electrons spinning in the same direction contain net magnetic moments and are weakly attracted to magnets.

The nucleus has a positive charge and is spinning. This generates a small magnetic field. The nucleus therefore possesses a magnetic moment, m, which is proportional to its spin,I. The constant, g, is called the magnetogyric ratioand is a fundamental nuclear constant which has a different value for every nucleus.

I thought that only way a nucleus can be NMR active is when the atom has an odd mass, which means that there is an odd number of protons or neutrons and an even number of the other particle.

Most particles with spin possess a magnetic moment. This magnetic moment can be experimentally observed, by passing the particles through an inhomogeneous magnetic field in a Stern-Gerlach type experiment, or by measuring the magnetic fields generated by the particles themselves.

Identifying Spin Direction

1. Determine the number of electrons the atom has.
2. Draw the electron configuration for the atom. See Electronic Configurations for more information.
3. Distribute the electrons, using up and down arrows to represent the electron spin direction.

Formula used: μ=√4s(s+1), μ=√n(n+2) To calculate spin only magnetic moment, μ=√4s(s+1) where s = Spin magnetic moment. μ=√n(n+2) where n = Number of unpaired electrons.

The Spin Quantum Number (ms) describes the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum. Because angular momentum is a vector, the Spin Quantum Number (s) has both a magnitude (1/2) and direction (+ or -).

Ralph Kronig had come up with the idea of electron spin several months before George Uhlenbeck and Samuel Goudsmit. Most textbooks credit these two Dutch physicists with the discovery.

Samuel Goudsmit

Spin quantum number (s) Spin quantum number denotes the spin of the electron on its own axis. It is denoted by ‘s’. It can have only two values(+½ and -½).

Quantum Numbers

• To completely describe an electron in an atom, four quantum numbers are needed: energy (n), angular momentum (ℓ), magnetic moment (mℓ), and spin (ms).
• The first quantum number describes the electron shell, or energy level, of an atom.
• The dynamics of any quantum system are described by a quantum Hamiltonian (H).

The Third Quantum Number: Orientation in Three Dimensional Space. The third quantum number, m l is used to designate orientation in space. The figure-8 shape with ℓ = 1, has three shapes needed to completely fill the spherical shape of an electron cloud.

The principal quantum number, n, describes the energy of an electron and the most probable distance of the electron from the nucleus. In other words, it refers to the size of the orbital and the energy level an electron is placed in. The number of subshells, or l, describes the shape of the orbital.

The principal quantum number n represents the relative overall energy of each orbital. The energy level of each orbital increases as its distance from the nucleus increases. The sets of orbitals with the same n value are often referred to as an electron shell.

There are four quantum numbers: n – principal quantum number: describes the energy level. ℓ – azimuthal or angular momentum quantum number: describes the subshell. mℓ or m – magnetic quantum number: describes the orbital of the subshell.

Rules Governing the Allowed Combinations of Quantum Numbers The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. The angular quantum number (l) can be any integer between 0 and n – 1. If n = 3, for example, l can be either 0, 1, or 2.

Electron orbital diagrams are a way of illustrating what energy level and orbital shape of the probable location of each of the electrons of an element. Use the periodic table below to keep track of where the s, p, and d blocks are located.

The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital.