Describe atomic structure and the historical development of atomic models. Use protons, neutrons, electrons, mass number, isotopes, and ions to interpret chemical symbols.
A lesson of Chemistry, in Atomic Structure and Periodicity, about 35 minutes.
By the end of this lesson, you will be able to read any isotope symbol, count protons, neutrons and electrons, explain what each historical experiment proved, and compute an average atomic mass.
Three Particles, Two Places
Particle
Charge
Mass (amu)
Where
proton
$+1$
$1$
nucleus
neutron
$0$
$1$
nucleus
electron
$-1$
$\approx 0$
around it
The nucleus holds essentially all the mass and almost none of the volume. An
electron weighs about $1/1836$ of a proton, so it contributes nothing worth
counting to the mass while occupying nearly all the space.
The proton count IS the element. Six protons is carbon, and nothing else can
be carbon. Change the neutrons and you have a different isotope of carbon; change
the electrons and you have an ion of carbon; change the protons and it is a
different element entirely.
$$\textbf{atomic number } Z = \text{protons}$$
$$\textbf{mass number } A = \text{protons} + \text{neutrons}$$
A neutral atom has equal protons and electrons, which is why the charges
cancel.
Reading the Symbol
$$^{A}{Z}\mathrm{X} \qquad ^{14}{6}\mathrm{C}$$
Mass number on top, atomic number below. Carbon-14 has $6$ protons and
$14 - 6 = 8$ neutrons.
The atomic number is redundant, because the symbol already says which element
it is. That is why $^{14}\mathrm{C}$ and "carbon-14" are both complete.
Neutrons are always found by subtracting: $A - Z$. There is no other way, and
the periodic table never lists them, because they vary between isotopes of the
same element.
A positive charge means electrons were LOST, which is backwards from
intuition until you remember that electrons are the negative ones. Removing
negatives leaves a surplus of positive.
All carbon, all six protons, with $6$, $7$ and $8$ neutrons.
Chemistry is decided by electrons, so isotopes behave almost identically.
$^{14}\mathrm{C}$ takes part in exactly the same reactions as $^{12}\mathrm{C}$,
which is what makes radioactive tracers possible: the body cannot tell the
difference, so a labeled molecule follows the ordinary pathway and can be
followed with a detector.
But nuclear stability is completely different. $^{12}\mathrm{C}$ is stable
forever and $^{14}\mathrm{C}$ decays with a half-life of $5730$ years, which is
what makes carbon dating work.
That split is the whole point of the isotope concept, and it is why
$^{235}\mathrm{U}$ and $^{238}\mathrm{U}$ have to be separated by physical means:
no chemical reaction can tell them apart.
Average Atomic Mass
The periodic table says chlorine is $35.45$ amu, and no chlorine atom weighs
that. It is a weighted average over the natural abundances.
Chlorine is about $75.8%$ $^{35}\mathrm{Cl}$ and $24.2%$ $^{37}\mathrm{Cl}$:
$$35 \times 0.758 + 37 \times 0.242 = 35.48$$
The average lands nearer the more abundant isotope, always, and that gives you
a free check: an average of $35.45$ sitting close to $35$ says most chlorine is
$^{35}\mathrm{Cl}$, without knowing any percentages.
Use decimal fractions, not percentages, in the calculation. Multiplying by
$75.8$ instead of $0.758$ gives an answer about a hundred times too large, which
is at least an obvious error.
Worked Example 1: Average Atomic Mass
Copper is $69.2%$ $^{63}\mathrm{Cu}$ and $30.8%$ $^{65}\mathrm{Cu}$.
What Each Experiment Actually Proved
The atomic model was not guessed. Each version was forced by an experiment that
the previous model could not explain.
Dalton, 1803. Matter is made of indivisible atoms, and compounds combine in
fixed whole-number ratios. Explained why water is always $\mathrm{H_2O}$.
Thomson, 1897. Cathode rays bent in a magnetic field and carried negative
charge, so atoms contain smaller negative particles. Atoms are divisible,
which Dalton had denied.
Rutherford, 1911. Alpha particles fired at gold foil mostly passed straight
through, and a very few bounced almost straight back. The positive charge and
the mass are concentrated in a tiny nucleus, and the atom is mostly empty
space. Thomson's evenly spread positive charge could not deflect anything that
hard.
Bohr, 1913. Heated elements emit only specific colors, not a continuous
spectrum. Electron energies are quantized, sitting in fixed levels rather
than anywhere at all.
Quantum model, 1926. Electrons are described by probability clouds called
orbitals rather than orbits. Bohr's circular paths worked only for hydrogen.
Each model was not wrong so much as incomplete, and each survived until an
experiment found its edge. That is the pattern of how physical science actually
develops, and it is worth more than the dates.
Sort It: Which Experiment Showed It
Worked Example 2: Ions
Worked Example 3: Putting It Together
$$^{56}_{26}\mathrm{Fe^{3+}}$$
Common Mistakes
Mistake 1: Reading the mass number as the neutron count
Neutrons are $A - Z$. The mass number includes protons.
Mistake 2: Thinking a positive ion gained protons
It lost electrons. Protons never change.
Mistake 3: Expecting an atom to weigh the table's average
$35.45$ is a weighted average over isotopes; no single atom has it.
Mistake 4: Using percentages instead of decimals
$0.758$, not $75.8$.
Mistake 5: Thinking isotopes react differently
Chemistry is electrons. Isotopes differ nuclearly, not chemically.
Where This Goes Next
Rutherford's result raised a problem his model could not survive, and solving it
required new physics.
An orbiting electron is an accelerating charge, and classical electromagnetism
says an accelerating charge radiates energy. A radiating electron would spiral
into the nucleus in about $10^{-11}$ seconds. Every atom should collapse
instantly, and obviously none do.
Bohr's fix was to declare certain orbits stable by decree, which worked
numerically for hydrogen and explained nothing. Quantum mechanics replaced it
properly: an electron is described by a wavefunction, and the allowed energies
fall out of the mathematics rather than being imposed. There is a lowest energy
state below which it cannot go, so there is nowhere left to spiral to.
That is the last lesson of this history. Each model was overturned by an
experiment it could not explain, and the current one will be too if something
finds its edge. Atoms are not the indivisible things Dalton described, protons and
neutrons are themselves made of quarks, and the useful question is never "is this
model true" but "where does this model stop working".
The next lesson takes the quantum picture seriously and works out where the
electrons actually go, which turns out to explain the entire shape of the periodic
table.
Check Your Understanding
Five of them, no instructions this time.
Summary
Protons decide the element, neutrons decide the isotope, electrons decide the
charge.
$$Z = \text{protons} \qquad A = \text{protons} + \text{neutrons} \qquad \text{neutrons} = A - Z$$
A positive ion LOST electrons. Protons never change in chemistry.
Isotopes are chemically identical and nuclearly different, which is why
tracers and carbon dating both work.
Average atomic mass is weighted by abundance, so it always sits nearer the
commoner isotope.
Each atomic model was forced by an experiment the previous one could not
explain.