Kinetic energy is a big deal in atomic and solid-state
physics.
Some folks have mentioned "exchange" and "exclusion".
That's entirely correct as far as it goes, but when
explaining this to HS students I wouldn't start there.
I would start with kinetic energy. That's something
they already know about.
This is the world's simplest QM calculation: Particle
in a box. Wavefunction has some curvature. Smaller
box means more curvature. Momentum is proportional
to wavenumber. KE is p^2 / 2m. Draw the graph.
That's a fair number of steps, but each step is easy
to understand.
For a single particle in a box, you don't even need
to worry about exchange and exclusion, and at the
most elementary level I wouldn't even worry about
that. For a multi-particle system, you definitely do
need to worry about such things. They make a large
quantitative change in the /amount/ of kinetic energy,
but they don't change the qualitative story. Let's
not lose the forest in the trees: The name of the
forest is still kinetic energy.
There is a common misconception that force is the
gradient of "potential" energy. In this case, the
force that you feel when you try to compress solid
matter is the gradient of the microscopic /kinetic/
energy. Particle in a box. You're trying to make
the box smaller. Energy goes up. This explains
more than 100% of the force that you feel; the
gradient of the microscopic potential energy (i.e.
electrostatics) is in the other direction, helping
you to squeeze on the box.
The size of an atom can be understood in terms of
equilibrium between the inward terms (electrostatics)
and the outward terms (kinetic energy). Using this
foundation, you can get an estimate for the Bohr
radius using little more than dimensional analysis,
which is a nifty almost-quantitative result.
And this imparts some fundamental conceptual understanding.
It immunizes you from the qualitatively-wrong ideas in
the Next Generation Science Standards.