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If I hit an object with a pen for example, does the pen touch the atoms on the surface of the object? Won't it damage the atoms? If I can't touch it, then where does the sound come from?

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Let's analyze this problem. Very idealistically, the energy with which the pen of mass $m$ hits the object is given by $$ E = \frac{1}{2} I \omega^2,$$ where $I$ is the moment of inertia defined about an axis and $\omega$ is the angular velocity of the pen. Or even $$E = mgh,$$ where $g$ is the contribution from gravity and $h$ is the height from which it was dropped. Now let this setup hit the object and we find that if the object were classical with some defined repulsive potential $V_{obj}$, then the objects can touch iff $E \sim V_{obj}$, up to a few small corrections. Try and work out the answer for a pen of weight a few grams hitting the object with some velocity. You will find that this is not even close to overcoming the potential barrier due the electrons. This is because if the two atoms try to get too close to each other, they will experience a strong repulsive force. This force is quite strong, at least stronger than the energy dispersed by hitting a pen to an object.

When you hit an object with a pen or similar scenarios, the energy from the interaction is partially absorbed by the two objects while some of the energy gets converted to sound. If you tried to do the same experiment in something like a vaccum, you wont be able to transfer the energy into the surrounding medium aka air, and therefore you won't be able to hear a sound.

Alternatively, do the same thing, with the experiment placed in different gaseous media - you will record sounds of different frequencies.

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A short answer could be the following. Touching means experiencing some kind of reaction force, which is the macroscopic translation of the repulsive forces between the pen atoms and the object atoms. So, yes, you can touch object. On the other hand no damage is done to the atoms, as the coulomb forces that hold together atoms are much stronger than the force you can apply to the object. In the best case, you can rip off some loosely bound electrons, which results in static charging of the object. You can of course break the object, but that does not damage atoms, but only the bonds between them.

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