How can electron affinity be negative?
Electron affinity can be negative if the process releases energy.
Electron affinity is the enthalpy change for the process:
The incoming electrons will experience a force of attraction with the effective charge of the nucleus. This charge is less than the actual nuclear charge since the inner electrons provide a "shielding" effect.
It requires work to separate two oppositly charged particles. Conversely, energy is released in bringing together two such particles.
An incoming electron will go into the outer
The electron will have kinetic energy. As it slams into the atom this energy is transferred to the atom and heat is released. The relative amount of heat and light produced is about 50:50.
This is why reactions such as sodium burning in chlorine can be so spectacular.
Please note that electron affinity is only one step in the overall energy cycle which dictates whether or not the process will be exothermic.
The 2nd electron affinity can be endothermic e.g:
This is because we are forcing two negative charges together, which requires energy.