Description
Return parent times exp(-constant times time), radiogenic daughter using -parent times expm1 of the same exponent, and initial plus radiogenic daughter.
An isotope ratio depends on which isotope is in the numerator and denominator. Delta notation compares a ratio with a reference on a per-mil scale, while mixing and decay models require explicit amount and system assumptions.
Return parent times exp(-constant times time), radiogenic daughter using -parent times expm1 of the same exponent, and initial plus radiogenic daughter.
When to use this tool
Use Isotope Parent Daughter Decay One Step when you need a stated isotope-reference, mixing, or one-step decay calculation.
How to use the tool and how it works
- Enter initialParent, initialDaughter, decayConstant, time. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingParent, radiogenicDaughter, totalDaughter. Use the output convention below.
Require nonnegative initialParent, initialDaughter, decayConstant, and time. Return parent times exp(-constant times time), radiogenic daughter using -parent times expm1 of the same exponent, and initial plus radiogenic daughter.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initialParent | Initial Parent | Required. Finite number; minimum 0. |
| initialDaughter | Initial Daughter | Required. Finite number; minimum 0. |
| decayConstant | Nonnegative rate in inverse units of time. | Required. Finite number; minimum 0. |
| time | Time | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingParent | Remaining Parent | Required. Finite number. |
| radiogenicDaughter | Daughter produced by modeled decay, excluding initial daughter. | Required. Finite number. |
| totalDaughter | Total Daughter | Required. Finite number. |
{
"input": {
"initialParent": 100,
"initialDaughter": 20,
"decayConstant": 0.6931471805599453,
"time": 1
},
"output": {
"remainingParent": 50,
"radiogenicDaughter": 50,
"totalDaughter": 70
}
}Limitations and assumptions
- Time and inverse-time decay constant must be compatible. The model assumes a closed one-parent-to-one-stable-daughter system without branching, daughter decay, gain, or loss; it does not infer an age from measurements.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the appropriate reference materials and full isotope model for interpretation. Preserve ratio orientation, reference scale, denominator-isotope weighting, uncertainty, and any open-system or fractionation effects.
References
Similar or alternative tools
- Isotope Ratio Mixing Weight
Scale both amounts by their maximum, form normalized weights, and interpolate the two ratios stably; return mixedRatio and firstWeight.
- Isotope Delta To Ratio Standard Term
Return sampleRatio equal to standardRatio times (1+deltaPerMil/1000).