[Djanoko]

When Na reacts with Cl to form NaCl, the reaction gives off a lot of heat and a bright yellow light.

If some of the mass of Na and Cl is transformed into energy during the reaction, then the final product NaCl should be lighter than the sum of its elements Na and Cl. It should be that something went missing during the reaction. But that's not the case, as the same number of protons, neutrons and electrons is found in NaCl as in its separate constituents Na and Cl. So what produces the heat and the light?

[Hunter2]

It's the built up of the ionic bond between the sodium and chloride ions.its a redoxreaction. Also the built up of the crystal lattice.
Sodium get oxidised and chlorine reduced.
Before we had only metallic bond in sodium and covalent bond in Chlorine.
Borne Haber process

https://www.sarthaks.com/?qa=blob&qa_blobid=11054596370432429967

[Borek]

Technically E=mc², so yes, we should observe some change in mass. Trick is, it is so small it is unmeasurable (way beyond accuracy of our best weighing methods).

Note: it is not like change in the mass means change in the number of constituting elements. Mass defect observed in nuclei occurs despite the number of neutrons and protons being unchanged in nuclear reactions.

[Corribus]

Broadly, the release of heat is primarily due to conversion of chemical potential energy into kinetic energy. Isolated atoms have high potential energy, and when they react, they form a new complex with lower potential energy. That loss of potential energy is converted mostly into kinetic energy in the form of heat. Strictly speaking, entropy is involved in the change in thermodynamic potential (Gibbs energy), so we can't just think in terms of heat production/loss. I'm not sure why conversion of mass to energy got brought into this - for chemical processes, it is fair to assume that mass is conserved and energy only changes forms.

The yellow light is due to what is called the sodium D-line. The reaction between sodium and chlorine is so exothermic that it produces some electronically excited sodium atoms, which quickly relax (dump their excess energy) by emitting light. Due to selection rules, the light energy has to match the energy gap between atomic orbitals of sodium. Sodium has two main transitions that are closely spaced at around 589 nm, collectively called the sodium D line. We perceive light of this wavelength as bright yellow. It is the same reason that sodium gives a yellowish color in a flame test, it is responsible for the yellow color of yellow fireworks, and it is why a cucumber pickled in brine will glow bright yellow if you run a current through it. Note that different elements give rise to different color - the yellow is unique to sodium.

[Djanoko]

Thanks @Corribus for your comprehensive explanation!