Describe the amount of time needed for complete ecosystem recovery

A recovery is hugely dependent on a number of factors, and the time needed may vary from months to hundreds of years.

The parameters that need to be considered:

type of ecosystem - terrestrial or aquatic; if aquatic - stagnant or flowing body of water; fresh water, salt water, or brackish; tidal or stable; etc.
productivity - may be high, low, or somewhere in between; length of the growth season, which may vary from several weeks to year-round;
climate - tropical, subtropical, temperate, subpolar, polar;
amount of precipitation;
seasonality - one, two, or four seasons; duration of seasons;
kind of damage - disturbance, devastation (fire or volcanic ash); toxic materials; overpopulation and population explosion; elimination of species; extent of damage (area and severity).
migratory potential of species that are capable of re-populating the area.
resilience of the ecosystem - how much soil, how resistant it is to erosion.
A fast flowing stream may recover quickly from a single disruptive event, such as influx of noxious materials, especially if it can be populated from up-stream areas. On the opposite end there are old-growth forests, that may take hundreds of years to re-form the interactions between plants, fungi, and lichens, if a patch of a forest was completely devastated or subjected to clear cutting. On the other hand, the effect of a brush fire in a forest may be hardly noticeable after one growing season. A tropical forest typically has a thin layer of soil and can undergo denudation after clearcutting - and a complete recovery may take very long time, if it is possible at all. Tundra may recover slowly, because of a very short growth season; alpine ecosystems are typically fragile, easy to damage, and slow to recover.

Noble gases is far right