is the weak nuclear force what binds atoms together to make molecules?
No. The weak nuclear force is responsible for reactions that occur inside the nucleus. What 'binds' atoms together to form molecules is largely decided by the electrostatic forces.
so what is the difference between strong and weak nuclear force
The strong nuclear force is responsible for keeping the protons of a nucleus from repelling eachother and flying apart since like charges repel. The weak nuclear force is is the force which mitigates beta decay, the transmutation of quarks into other sub atomic particles via massive W & Z bosons. Check out Feynman diagrams relating to beta decay and it will easily show you how a proton becomes a neutron via this process. Hope that helps.
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