---
title: "Isotope dilution"
chunk: 1/2
source: "https://en.wikipedia.org/wiki/Isotope_dilution"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:44:05.958864+00:00"
instance: "kb-cron"
---

Isotope dilution analysis is a method of determining the quantity of chemical substances. In its most simple conception, the method of isotope dilution comprises the addition of known amounts of isotopically enriched substance to the analyzed sample. Mixing of the isotopic standard with the sample effectively "dilutes" the isotopic enrichment of the standard and this forms the basis for the isotope dilution method. Isotope dilution is classified as a method of internal standardisation, because the standard (isotopically enriched form of analyte) is added directly to the sample. In addition, unlike traditional analytical methods which rely on signal intensity, isotope dilution employs signal ratios. Owing to both of these advantages, the method of isotope dilution is regarded among chemistry measurement methods of the highest metrological standing.
Isotopes are variants of a particular chemical element which differ in neutron number. All isotopes of a given element have the same number of protons in each atom. The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table.

== Early history ==

Analytical application of the radiotracer method is a forerunner of isotope dilution. This method was developed in the early 20th century by George de Hevesy for which he was awarded the Nobel Prize in Chemistry for 1943.
An early application of isotope dilution in the form of radiotracer method was determination of the solubility of lead sulphide and lead chromate in 1913 by George de Hevesy and Friedrich Adolf Paneth. In the 1930s, US biochemist David Rittenberg pioneered the use of isotope dilution in biochemistry enabling detailed studies of cell metabolism.

== Tutorial example ==

Isotope dilution is analogous to the mark and recapture method, commonly used in ecology to estimate population size.
For instance, consider the determination of the number of fish (nA) in a lake. For the purpose of this example, assume all fish native to the lake are blue. On their first visit to the lake, an ecologist adds five yellow fish (nB = 5). On their second visit, the ecologist captures a number of fish according to a sampling plan and observes that the ratio of blue-to-yellow (i.e. native-to-marked) fish is 10:1. The number of fish native to the lake can be calculated using the following equation:

  
    
      
        
          n
          
            
              A
            
          
        
        =
        
          n
          
            
              B
            
          
        
        ×
        
          
            10
            1
          
        
        =
        50
      
    
    {\displaystyle n_{\mathrm {A} }=n_{\mathrm {B} }\times {\frac {10}{1}}=50}
  

This is a simplified view of isotope dilution but it illustrates the method's salient features. A more complex situation arises when the distinction between marked and unmarked fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of marked fish from previous field experiments; and vice versa, where the amount of marked fish added contains a small number of unmarked fish. In a laboratory setting, an unknown (the "lake") may contain a quantity of a compound that is naturally present in major ("blue") and minor ("yellow") isotopic forms. A standard that is enriched in the minor isotopic form may then be added to the unknown, which can be subsequently analyzed. Keeping to the fish analogy, the following expression can be employed:

  
    
      
        
          n
          
            
              A
            
          
        
        =
        
          n
          
            
              B
            
          
        
        ×
        
          
            
              
                R
                
                  
                    B
                  
                
              
              −
              
                R
                
                  
                    A
                    B
                  
                
              
            
            
              
                R
                
                  
                    A
                    B
                  
                
              
              −
              
                R
                
                  
                    A
                  
                
              
            
          
        
        ×
        
          
            
              1
              +
              
                R
                
                  
                    A
                  
                
              
            
            
              1
              +
              
                R
                
                  
                    B
                  
                
              
            
          
        
      
    
    {\displaystyle n_{\mathrm {A} }=n_{\mathrm {B} }\times {\frac {R_{\mathrm {B} }-R_{\mathrm {AB} }}{R_{\mathrm {AB} }-R_{\mathrm {A} }}}\times {\frac {1+R_{\mathrm {A} }}{1+R_{\mathrm {B} }}}}
  

where, as indicated above, nA and nB represent the number of fish in the lake and the number of fish added to the lake, respectively; RA is the ratio of the native-to-marked fish in the lake prior to the addition of marked fish; RB is the ratio of the native-to-marked fish in the amount of marked fish added to the lake; finally, RAB is the ratio of the native-to-marked fish captured during the second visit.

== Applications ==
Isotope dilution is almost exclusively employed with mass spectrometry in applications where high-accuracy is demanded. For example, all National Metrology Institutes rely significantly on isotope dilution when producing certified reference materials. In addition to high-precision analysis, isotope dilution is applied when low recovery of the analyte is encountered. In addition to the use of stable isotopes, radioactive isotopes can be employed in isotope dilution which is often encountered in biomedical applications, for example, in estimating the volume of blood.

== Single dilution method ==

Consider a natural analyte rich in isotope iA (denoted as A), and the same analyte, enriched in isotope jA (denoted as B). Then, the obtained mixture is analyzed for the isotopic composition of the analyte, RAB = n(iA)AB/n(jA)AB. If the amount of the isotopically enriched substance (nB) is known, the amount of substance in the sample (nA) can be obtained:

  
    
      
        
          n
          
            
              A
            
          
        
        =
        
          n
          
            
              B
            
          
        
        
          
            
              
                R
                
                  
                    B
                  
                
              
              −
              
                R
                
                  
                    A
                    B
                  
                
              
            
            
              
                R
                
                  
                    A
                    B
                  
                
              
              −
              
                R
                
                  
                    A
                  
                
              
            
          
        
        ×
        
          
            
              x
              
                (
                
                  j
                
              
              
                A
              
              
                )
                
                  
                    B
                  
                
              
            
            
              x
              
                (
                
                  j
                
              
              
                A
              
              
                )
                
                  
                    A
                  
                
              
            
          
        
      
    
    {\displaystyle n_{\mathrm {A} }=n_{\mathrm {B} }{\frac {R_{\mathrm {B} }-R_{\mathrm {AB} }}{R_{\mathrm {AB} }-R_{\mathrm {A} }}}\times {\frac {x(^{j}\mathrm {A} )_{\mathrm {B} }}{x(^{j}\mathrm {A} )_{\mathrm {A} }}}}
  

Here, RA is the isotope amount ratio of the natural analyte, RA = n(iA)A/n(jA)A, RB is the isotope amount ratio of the isotopically enriched analyte, RB = n(iA)B/n(jA)B, RAB is the isotope amount ratio of the resulting mixture, x(jA)A is the isotopic abundance of the minor isotope in the natural analyte, and x(jA)B  is the isotopic abundance of the major isotope in the isotopically enriched analyte.
For elements with only two stable isotopes, such as boron, chlorine, or silver, the above single dilution equation simplifies to the following: