Step 1: Understanding the Question.
Biogeochemical cycles move elements between living organisms, soil, water, rock and the atmosphere. We need to pick which of carbon, nitrogen, phosphorus and sulphur moves the smallest mass through the atmosphere each year.
Step 2: Key Concept or Approach.
Whether an element has a large atmospheric flux depends mainly on whether it has a common, stable gas form. Elements with an abundant gas phase move huge amounts through the air every year, while elements that mostly stay locked in rocks, soil and water, with little or no gas phase, move only tiny amounts through the atmosphere.
Step 3: Detailed Explanation.
Carbon has a well known gas cycle: carbon dioxide is exchanged constantly between the atmosphere, plants, animals, oceans and soils through photosynthesis, respiration and combustion. This gives carbon a very large atmospheric flux.
Nitrogen makes up about \(78\%\) of the atmosphere as \(N_2\) gas, and large amounts also move as ammonia, nitrous oxide and other nitrogen gases through fixation, nitrification, denitrification and volcanic and industrial emissions. This also gives nitrogen a large atmospheric flux.
Sulphur has gas forms too, such as sulphur dioxide and hydrogen sulphide, released from volcanoes, the ocean surface, decomposition and burning of fossil fuels, so sulphur also moves through the atmosphere in fairly large amounts, though generally less than carbon or nitrogen.
Phosphorus is different: it has essentially no common, stable gas phase under normal conditions. Almost all of the phosphorus cycle runs through rock weathering, soil, rivers, lakes and oceans, moving as dissolved or particulate phosphate rather than as a gas. The only way phosphorus enters the atmosphere at all is as dust particles or fine aerosols, which is a tiny mass flux compared to the gas-driven cycles of carbon, nitrogen and sulphur.
Step 4: Final Answer.
Because phosphorus lacks a significant atmospheric gas phase and its cycle is dominated by rock, soil and water pathways, it cycles the least mass per year through the atmosphere among these four elements.
\[ \boxed{\text{Phosphorus}} \]