What determines the slope on an isochron diagram?

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BlackTom AI · Accepted Answer

Question focus: isochron diagrams and what controls their slope.
Option a: 'Amount of parent isotope' — While the amounts change as aging proceeds, the slope of an isochron is not determined by how much parent is left at the moment. The slope encodes time elapsed, not the instantaneous quantity alone. Misconception: daten are about current quantities rather than the time-integrated decay relationship.
Option b: 'age' — This is the core idea. The slope of an isochron is directly related to the time elapsed since the system closed, i.e., the age. In radiometric dating, the mathematical relation between parent and daughter isotopes translates age into a slope on the plot (often through a function of decay constant λ and time t). Therefore, the slope serves as a proxy for the age of the sample.
Option c: 'Amount of product (daughter) isotope' — The amount of daughter accumulated is a consequence of the decay process over time, but it alone does not set the slope. Different ages could yield similar daughter amounts if initial conditions differ, so the slope is not determined solely by the current amount of daughter.
Option d: 'Initial isotopic ratio' — The initial ratio affects the intercept of the isochron line, not the slope. Isochron methods are designed so that samples with the same initial ratio align along a line whose slope encodes the age; the initial ratio shifts the line vertically, not its tilt. Therefore, the initial ratio governs intercept, not slope.

What determines the slope on an isochron diagram?

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