The question is ambiguous.
The primary force between distinct atoms that holds them together is the electromagnetic force (there's also gravity, but that's much much weaker). The communicating particle (aka "gauge particle") for the electromagnetic force is the photon.
Several forces play a part in holding an individual atom together. Electrons are bound to the nucleus by the electromagnetic force. The individual nucleons (protons and neutrons) are composed of quarks held together by the strong nuclear (or "color") force, and the nucleons are bound together in the nucleus by the residual strong nuclear force. The gauge particle for the strong force is known as the gluon.
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The force that holds atoms together is called the electromagnetic force. This force is a result of the attraction between positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus.
The electromagnetic field causes atoms to bind together to create molecules, and materials humans use everyday. So, to answer your question: The electromagnetic force, the positive/negative attraction between electrons and protons, causes atoms to bind together.
It depends on the atom. A charged atom's attraction is called electostatic forces.
The intermolecular attraction.
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the force of attraction that holds atoms together is a chemical bond
The force that holds atoms together is called a chemical bond. This bond is formed when atoms share or exchange electrons to achieve a stable configuration, allowing them to be held together in a molecule or crystal structure.
Covalent bond
A Chemical Bond