Neutrons don't have an electric charge, so they are not repelled by the negative electrons around the atom, or the positive protons in the nucleus. The strong nuclear force (which is much stronger than other forces, hence the name) holds protons and neutrons together in the nucleus, and keeps the new neutron there instead of it "bouncing" off.
SchiferlED t1_iu6cjvs wrote
Reply to comment by Sklifosovsky20 in ELI5: Does a nuclear explosion make other atoms radioactive or simply contaminates it? by Sklifosovsky20
Neutrons don't have an electric charge, so they are not repelled by the negative electrons around the atom, or the positive protons in the nucleus. The strong nuclear force (which is much stronger than other forces, hence the name) holds protons and neutrons together in the nucleus, and keeps the new neutron there instead of it "bouncing" off.