How is the growth of land plants proof that there is carbon in the atmosphere? How does carbon exist in the atmosphere, biosphere, and geosphere all at the same time? (Site 1 )

Plants take the CO2 from the atmosphere which is used in Calvin's cycle to synthesize organic compounds that end up building the plant. This fact can be proved by marking the atmospheric CO2 with radioactive isotopes of carbon, afterwards using a Geiger counter the plant will present radioactivity.

The carbon in the atmosphere is most commonly found in the form of CO2

it has a concentration of 0.04%.CO2 is a byproduct of aerobic respiration

or combustion, for example, C6H12O6+6O2-->6CO2+6H2O. The CO2 is then used by plants in photosynthesis as mentioned earlier.

Carbon is present in the biosphere because all life is made of carbon.

Carbon is present in the geosphere most commonly under the form of hydrocarbons like methane(CH4). The carbon present in geosphere is a result of organisms decay and metabolic byproducts. For example, methanogen bacteria synthesize methane in anaerobic conditions reducing hydrogen in the presence of CO2(CO2+4H2⇒CH4+2H2O). Carbon in the geosphere can also be found in coal that becomes diamond under extreme pressure and temperature.

for  example, forests have higher evapotranspiration than other ecosystems,  such  as grasslands, because of their deeper roots and greater leaf area. thus forests have a net moistening effect on the atmosphere and become a moisture source for downwind ecosystems.