584 FRED M. UBER 



Whenever an isotopic element being studied is lepresented by a 

 single atom in the ionized test particle, even though one or more other 

 elements may also be present, the concentration of the element under 

 test can be calculated usually by means of an appropriate substitu- 

 tion in equation (3). Of the common stable isotopes encountered in 

 biological studies, the measurement of sulfur, either as sulfur dioxide 

 or as hydrogen sulfide, furnishes a second example. 



If the isotopic element being measured occurs twice or more in the 

 test molecule, the calculations are somewhat more involved. For 

 example, when N^^ determinations are made using the diatomic nitro- 

 gen molecule, probabiUty considerations indicate the following molec- 

 ular configurations: WN'S W^W, W"^'', and WW. If the 

 concentration of N^^ in atom per cent equals P, the complementary 

 atomic concentration of N^* is (100 — P). The relative molecular 

 concentrations at equilibrium of the three molecular species with 

 masses 28, 29, and 30 will be (100 - Py, 2P(100 - P), and P\ 

 respectively. Since the ionization current readings of the mass 

 spectrometer will be proportional only to the concentrations of the 

 molecular ions having masses 28, 29, and 30, the ratio of the corrected 

 peak readings for masses 28 and 29 will be expressed as follows: 



28 _ mass 28 peak _ (100 - P)^ ^ 100 - P .^. 



'' ~ mass 29 peak " 2P(100 - P) ~ 2 P 



The solution of this equation indicates that the concentration, P, of 



N^^ can be calculated from measurements at only two mass numbers. 



That is: 



100 ..s 



P = —55 atom per cent y'^) 



2 llR + 1 ^ 



When the height of the peak at mass 30 indicates a sufficiently high 

 concentration, the calculation can be based also on either of the other 

 two ratios, as indicated by the following equations : 



llR = — — -, or P = 29p ■ ^ atom per cent (6) 



. (100 - py ^ 100 ^ ^ (^. 



R = -: or P = 2^— atom per cent U; 



'''" P2 ""'^ ~foR+l 



Determinations of P by two independent methods serve as a valuable 

 check on the equilibrium attained by the ionic test particles and help 



