Do atoms have more energy when moving?

Atoms are always moving. If there center-of-mass does not seem to be moving relative to some reference there is the internal movement of the electrons and the vibrational modes.

But yes, when they are moving, the velocity implies kinetic energy/momentum = mv^2.
It’s pretty tough to say anything about a single atom of anything, at least because of the Heisenberg effect… observing the momentum is going to change it.

what I am trying to say is can we know it’s moving by its energy alone not the fact that we can see/ measure it moving

Atoms have kinetic energy according to K = ½ m*v^2 as usual. As you raise temperature this average kinetic energy rises as the atoms & molecules speed up. We call this energy heat, but it ultimately derives from kinetic energy of individual atoms.

The kinetic theory of heat and matter was established and proven in the second half of the 19 Century with a long series of convincing experiments, demolishing the previous (and erroneous) hypothesis of “calor” or “phlogistin.”

@inunsure You have to measure something. If you want to measure “energy” alone, you have to define what it is, and then you have to measure it. To measure it, you have to interact with it in some way. Even “seeing” is an interaction. Of course, we can’t see atoms with the eye because they are too small. But we can build detectors that would detect photons coming from atoms, if they emit any.

We can’t know an atom moves in the same way we can see that a horse or a car moves. We have to have a model of “movement” on the atomic level and then build a detector that measures the impact of an atom hitting it. From this, we can infer movement. We can develop support for a model of atomic movement.