1.1. (Very) Brief Refresher of the Basics

Recall that elements typically consist of several different isotopes. Isotopes of an element all have the same number of protons but differ in the number of neutrons. For example, the element Hydrogen exists primarily as three isotopes (Figure 1.1): protium (1 proton, 0 neutrons; 99.985% of hydrogen atoms), deuterium (1 proton, 1 neutron; 0.015% of hydrogen atoms), and tritium (1 proton, 2 neutrons; trace amounts).

Figure 1.1 – Isotopes of Hydrogen.

Recall that all charged particles, such as electrons and proton-containing nuclei, can be described using a series of quantum numbers. One of these quantum numbers describes the “spin” (s, spin angular momentum) of the particle (Figure 1.2).

Figure 1.2 – Representation of Spin on a Generic Charged Particle.

The spin quantum number depends on both mass and charge. As a result, all electrons have the same spin number (½). Conversely, different isotopes of the same element have different masses and do not have the same spin number. For example, protium and tritium have the same spin value (½), but deuterium has a different value (1).

Finally, recall that spin quantum numbers lead to different possible states for the particles. These are sometimes referred to as spin magnetic quantum numbers, m_s. Values for m_s range from +s to –s at integer intervals. This means the particles can be in a certain number of states where each state has a m_s value of [s], [s-1], [s-2], … [-s] (Table 1.1). Functionally, the number of possible states increases by one every time the quantum spin number increases by ½.

Table 1.1 – Possible Values of m_s for Common Values of s.