Carbon dioxide, nitrogen and some oxygen are necessary for the growth of plants.
For the growth of plants, photosynthesis and respiration are vital, both these processes require these aforementioned gases. Soil air contains several gases such as oxygen, nitrogen, carbon dioxide and water vapour. This soil air has a higher proportion of carbon dioxide and less oxygen compared to the atmospheric air. Similarly, soil air has a higher amount of water vapour compared to atmospheric air while the amount of nitrogen is almost the same in atmospheric air and soil air.
For plants to grow, photosynthesis is the most important process which primarily is driven by carbon dioxide. Without this gas, plants cannot manufacture their own food. Apart from this, nitrogen is the gas, abundantly available in the atmosphere. However, it is not available in a form that can be used by them directly, hence the process of nitrogen fixation by some bacteria. Lastly, some oxygen, in some amount, comparatively, is also necessary for the growth of plants as they are living entities after all.
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