We see stones and they appear to be the same throughout our life time. Mountains also appear to not significantly change. So do mountains and stones decompose? What is the life span of a stone? After it decomposes, what does it turn into?
Mountains and rock do decompose or weather into sediment. A basic rock cycle overview shows the possible pathways between all three rock types (igneous, metamorphic, and sedimentary) how one type can be transformed into another. After a rock is weathered into sediment, that sediment can become a rock again.
Weathering rates of rock vary widely regional based on the following factors:
- Mineral composition of the rock (some minerals are less stable at surface conditions than others)
- Amount of plant life growing on the rocks and mountains. (Plant roots can be powerful chemical and physical weathering agent)
- Amount of precipitation (Chemical dissolution due to rainfall is a significant weathering factor for some rock types (carbonate rocks)
- Seasonal freezing periods. (Ice expansion in cracks and fractures can weaken rocks over very short periods of time.
- Temperature range of the region. (I believe diurnal temperature differentials specially in high mountain deserts has a specific weather impact on some rock types).
- Local earthquakes and volcanic activity.
- Erosion due to water (streams, rivers, lakes, and oceans).
- Erosion due to glaciers and ice flows.
You can get an estimate of weathering rates of different rock types for a local region by careful examination of cemetery gravestones.
Millions of years.
While it also depends on what kind of rock you're asking about, @GaryKindel's answer above lists a number of other properties a rock has that will effect the time it will take to decompose.
So do mountains and stones decompose?
Yes, they do; but very slowly.
Over millions and sometimes billions of years, a rock will decompose into sediment. As stated above, and then again in @GaryKindel's answer, The rate that they will decompose at really depends on the rock.
For example; two types of rocks that will decompose quickly (still being hundreds of thousands of years or more) are listed below:
And some rocks that decompose very slowly:
What is the life span of a stone?
Rocks never die, they just change form. So they don't have a lifespan.
Rocks are always changing form, but too slowly to notice with you're eyes. In fact; rocks aren't even classified as living things. But all rock goes through three main stages:
The process these rocks go through is called the rock cycle.
There are also some substages:
Magma (Lava; molten rock)
Sediment or soil (microscopic rocks we cannot see; sorta like body cells)
After it decomposes, what does it turn into?
Well, more rock. Just in another stage of the rock cycle.
As mentioned above, rocks are always changing form, and they do go through a number of substages. But after a rock decomposes, it will become sediment, then after a number of years will compress into a form of sedimentary rock (e.g. Sandstone, shale, etc.).
And as @jamesqf mentioned above, some sedimentary rock can be crushed with your bare hands.