Atomic Structure

Imagine a sports stadium with a single marble sitting on the 50-yard line. The field is otherwise empty. So are the stands, concourses, parking lot, surrounding blocks. That is the scale of an atom: almost entirely empty space, with virtually all the mass packed into an incomprehensibly tiny center.

The marble is the nucleus. The empty space around it is where the electrons live, smeared out in cloud-like orbitals. Even though the nucleus is ~100,000× smaller than the atom, it contains 99.97% of the atom’s mass. Get this scale right and the rest of atomic and nuclear physics is much easier to picture.

The Three Subatomic Particles

Every atom is built from just three particles:

Protons and neutrons (collectively called nucleons) live in the nucleus. Electrons orbit far outside in the electron cloud. The electron’s mass is so small compared to the nucleons that it is essentially negligible for nuclear calculations.

Atomic Number and Mass Number

Two numbers define every nucleus:

• Atomic number (Z) - the number of protons. This determines the element. Every carbon atom has Z = 6. Every oxygen atom has Z = 8. Change Z and you change the element entirely.
• Mass number (A) - the total number of nucleons (protons + neutrons). A = Z + N, where N is the number of neutrons.

Nuclear Notation

The standard way to write a specific nucleus (nuclide) places the mass number as a superscript and the atomic number as a subscript, both to the left of the element symbol:

${}^{A}_{Z}\text{X}$ — for example, ${}^{12}_{6}\text{C}$ is carbon-12 (6 protons, 6 neutrons) and ${}^{14}_{6}\text{C}$ is carbon-14 (6 protons, 8 neutrons).

Since the element symbol already tells you Z (carbon is always 6), you will often see the shorthand carbon-12 or C-12. But on the MCAT, full nuclear notation appears frequently in decay equations, so practice reading it quickly.

Isotopes

Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different N, therefore different A). Carbon-12 and carbon-14 are both carbon - they have identical chemical properties because they have the same number of electrons. But carbon-14 has two extra neutrons, making its nucleus unstable and radioactive.

Most elements exist as a mixture of stable isotopes in nature. The atomic mass listed on the periodic table (for example, 12.011 for carbon) is the weighted average of all naturally occurring isotopes based on their abundance.

Atomic Mass Units

The atomic mass unit (amu or u) is defined so that one carbon-12 atom has a mass of exactly 12 u. By this definition:

• 1 proton ~ 1.0073 u
• 1 neutron ~ 1.0087 u
• 1 electron ~ 0.00055 u

One amu equals 1.66 x $10^{-27}$ kg. You will not need to convert between amu and kg often, but you should know the conversion exists - especially for mass defect and binding energy calculations later in this chapter.

Size Scales

Getting a feel for the relative sizes helps with intuition:

• Atom diameter: ~$10^{-10}$ m (1 angstrom)
• Nucleus diameter: ~$10^{-15}$ m (1 femtometer)
• Ratio: the nucleus is about 100,000 times smaller than the atom itself

This means the atom is overwhelmingly empty space. If the nucleus were the size of a marble (1 cm), the electron cloud would extend roughly 100 meters in every direction - about the length of a football field.