which are particles and waves simultaneously somehow

All quantum particles actually behave that way! It’s just harder to demonstrate (and observe) the more mass a particle has. Photons being massless make it very easy to demonstrate the effect. Also, if I remember correctly, light was the first particle that this was observed with and scientists thought it was unique to them (or maybe only the laymen did think so? I’m honestly not sure).

For example the electron microscope is a practical example of using electron’s wave-like qualities to show high-quality images.

I also seem to remember that the wave-particle duality was demonstrated on atoms, though I’m not very clear on the details.