why does the filament of bulb burn out when exposed to atmosphere whereas of a heater coil does not?

Answer 1

It's made of thinner more fragile metal. When a heater coil heats, it's thick enough the energy is dissapated before the metal starts to soften. The light bulb filiment however is extremely thin and in the presence of oxygen (air) will start to oxidize (burn) as it melts.

Answer 2

It is a matter of temperature and the total amount of material involved.

Over time, a heater element does "burn" (oxidize) out - it just doesn't go out in the same blast of smoke and glory that the small, fragile bulb filament does.