ICAR AIEEA PG Physical Science 14 July 2023 Shift-1 Paper

Irving-Williams series of chelate stability:

• Established by H. Irving and R. J. P. Williams (1953), the stability constants ($\log K$) of high-spin divalent transition metal complexes follow an invariant natural order across a wide variety of ligands:
  $$\text{Mn}^{2+} \lt \text{Fe}^{2+} \lt \text{Co}^{2+} \lt \text{Ni}^{2+} \lt \text{Cu}^{2+} \gt \text{Zn}^{2+}$$
• Comparing the four given divalent cations in decreasing stability order:
  $$\text{Cu}^{2+} \gt \text{Ni}^{2+} \gt \text{Co}^{2+} \gt \text{Zn}^{2+}$$
• This order arises from decreasing ionic radius and increasing ligand-field stabilization energy (LFSE), with copper achieving extra stability through the Jahn-Teller effect.

Mitscherlich's Law of Diminishing Returns (E. A. Mitscherlich, 1909):

• Mathematical equation: Mitscherlich formulated that the rate of increase in crop yield with respect to an increase in any growth factor ($x$) is proportional to the decrement from maximum attainable yield ($A$):
  $$\frac{dy}{dx} = (A - y)c$$
  Integrated form: $y = A(1 - e^{-cx})$.
• Justus von Liebig formulated the qualitative Law of the Minimum (1840).
• Bernhard Baule introduced the concept of Baule units (yielding $50\%$ of maximum).
• Roger H. Bray modified Mitscherlich's equation for mobile vs immobile soil nutrients.

Historical discoveries of plant nutrient essentiality:

• Molybdenum (Mo): Proven essential by D. I. Arnon and P. R. Stout in 1939: (A)-(III).
• Zinc (Zn): Proven essential for higher plants by A. L. Sommer and C. B. Lipman in 1926: (B)-(IV).
• Julius von Sachs and Wilhelm Knop: Developed hydroponics and nutrient solutions establishing the essentiality of major macro-nutrients: (C)-(I).
• Joseph Priestley: Demonstrated through bell jar experiments (1771) that plants purify air fouled by animal respiration / combustion, linking carbon assimilation: (D)-(II).