Equations for Following Nutrient Transformations in Soil, Utilizing Tracer Data

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Abstract
Theoretical equations are derived, for utilization of tracer data, for determining rates of mineralization m and immobilization i of plant nutrients in soil. The equations for a particular nutrient are urn:x-wiley:03615995:saj2sssaj195403615995001800010009x:equation:saj2sssaj195403615995001800010009x-math-0001 urn:x-wiley:03615995:saj2sssaj195403615995001800010009x:equation:saj2sssaj195403615995001800010009x-math-0002 where m = mass of immobile atoms mineralized per unit time per unit mass of soil (mineralization rate); i = mass of mineral atoms immobilized per unit time per unit mass of soil (immobilization rate); H0 = mass of tracing (heavy, or radioactive) mineral atoms per unit mass of soil at time t = O; M0 = mass of tracing, plus non‐tracing mineral atoms per unit mass of soil at time t = O; H = mass of tracing mineral atoms per unit mass of soil at time t = t; M = mass of tracing, plus non‐tracing mineral atoms per unit mass of soil at time t = t; t = time lapsed between measurements for H0, M0 and H, M; log = logarithm to base e or to base 10 for the equations for i ≠ m and to base e for the equation for m = i; e = 2.718.The equations for m and i, and some others which are also given, are all only valid if M0 and M are small compared to the amount of material which is being mineralized; and if i and m are constant during time t. The equations are applied to some nitrogen transformation data, with heavy nitrogen as the tracing element. The equations may also find application in studies of phosphorus and potassium fixation and release, with radioactive materials as the tracing elements. For numerical work, equations [a] and [b], although correct, should be replaced by equations [10] and [11] in the text if m > i.

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