04 Atomic Structure and Isotopes

The atom: particles and counting

An atom has a small, dense nucleus surrounded by electrons. The nucleus contains positively charged protons and neutral neutrons; negatively charged electrons occupy the region around it. Protons and neutrons each have a mass close to $1\,\mathrm{u}$, while an electron’s mass is about $\frac{1}{1836}$ of a proton’s. Consequently, nearly all an atom’s mass is in its nucleus.

The atomic number, written as $Z$, is the number of protons and determines the element. In a neutral atom, the number of electrons equals the number of protons. The mass number, written as $A$, counts the protons and neutrons together:

To find the neutron count, subtract the atomic number from the mass number:

For example, a neutral sodium-23 atom has $11$ protons, $12$ neutrons, and $11$ electrons. Its nuclear notation is ${}^{23}_{11}\mathrm{Na}$. The lower-left number gives $Z$, and the upper-left number gives $A$.

Takeaway: Protons identify the element; protons plus neutrons give the mass number.

Isotopes and average atomic mass

Isotopes are atoms of the same element with different numbers of neutrons. Because they have the same number of protons, they share the same elemental identity. For example, carbon-12 and carbon-13 each have $6$ protons, but carbon-12 has $6$ neutrons while carbon-13 has $7$. Some isotopes are radioactive.

The mass number is a count of nuclear particles, not a measured atomic mass. An isotope’s measured mass is generally not a whole number; nuclear binding energy affects the mass of its nucleus. The unified atomic mass unit is defined so that a carbon-12 atom has a mass of exactly $12\,\mathrm{u}$.

The value commonly listed for an element on the periodic table is a weighted average of the masses of its naturally occurring isotopes. Each isotope’s contribution depends on its fractional abundance. For two isotopes:

Natural carbon is about $98.93\%$ carbon-12 and $1.07\%$ carbon-13. Using isotope masses of $12.0000\,\mathrm{u}$ and $13.0034\,\mathrm{u}$, respectively, gives:

This average describes the isotope mixture, not the mass of every individual carbon atom. If the relative abundances changed, the average would change as well.

Takeaway: Isotopes differ in neutron count, while an element’s listed atomic mass reflects the masses and abundances of its isotopes.

How evidence refined atomic models

Atomic models changed as experiments revealed evidence that earlier models could not explain. Dalton’s atomic theory helped account for patterns in chemical reactions and the simple whole-number ratios in compounds. Its claim that atoms were indivisible had to be revised as internal structure was discovered.

In cathode-ray experiments, J. J. Thomson observed that rays were deflected by electric and magnetic fields and behaved as negatively charged particles. Their properties were consistent across different electrode materials, supporting the conclusion that electrons are constituents of atoms. Thomson proposed a model in which electrons were embedded in diffuse positive charge.

In the gold-foil experiment, Geiger and Marsden directed positively charged alpha particles at thin gold foil. Most passed through with little deflection, while a small number deflected sharply, some back toward the source. Rutherford’s nuclear model explained this pattern: an atom is mostly open space, with positive charge and most of its mass concentrated in a tiny nucleus.

In 1932, James Chadwick showed that the nucleus contains a neutral particle with a mass similar to a proton’s. This neutron helped explain how atoms of the same element can have different masses: their nuclei can contain different numbers of neutrons.

The modern model retains the nucleus but does not treat electrons as tiny planets following fixed paths. Quantum mechanics describes electrons using orbitals, which represent regions where electrons are likely to be found. Measurements including atomic spectra support this model.

Takeaway: Each new model addressed evidence that earlier models could not fully explain, while retaining useful parts of previous explanations.

• Thomson’s electron

• Rutherford’s nucleus

• Chadwick’s neutron

• orbital