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Cyclotron isotopes and radiopharmaceuticals—XXIV. Titanium-45
International Journal of Applied Radiation and Isolopcs, 1978. Vol. 29~ pp. 115 I [6. 0020-70SX/7S/0201-0115 $02.00/0 © Pergamon Prcss Ltd. Printed in Great Britain
Cyclotron Isotopes and Radiopharmaceulicals--XXl V.* Titanium-45? (Received 20 M a y 1977)
Introduction
TITANIUM-45 has a half-life of 3.05 hr and decays primarily (85%) by positron emission with EB,~x = 1.04 MeV. Low abundance ( < 1 % ) g a m m a emissions of 0.721, 1.237, 1.411 and 1.665 MeV are also present. The nuclide decays to 4SSc [a stable isotopetl)]. The decay characteristics are appropriate for detection on a positron camera, and the nuclide m a y be suitable for transaxial reconstruction tomography should an appropriate radiopharmaceutical be developed. In many respects 45Ti may be an ideal nuclide for tracing of biological functions and toxicological studies of environmental pollutants. The role of titanium as an essential trace element in the h u m a n body is controversial ~2-4~. Its role in biochemical processes has not been ascertained, although it is found in considerable levels in the body °~. According to BERNHEIM and BERNHEIM15~ titanium is thought to play a role in the oxidation of certain thio-compounds to sulfonic acids. VOINORt6) found that the addition of titanit/m sulfate to the daily diet of blood donors somewhat accelerated the regeneration of serum proteins and raised the erythrocyte count. However, h u m a n studies on titanium and its c o m p o u n d s are few~2'~'sk The presence of the metal in fairly high concentration in the h u m a n brain has been demonstrated 19). The metal is found in the lung of newborns and the a m o u n t increases with age ~3~. Workers exposed to TiO 2 have a high incidence of a lung disease called titantiosis ~2~. Elevated concentrations of titanium were found in patients with cystic fibrosis t~ o~ and in the leukocytes of patients with lymphoblastic leukaemia ~ ) . Titanium has also been found in higher than normal concentrations in cerebral tumors t~-'). Patients with bladder tumors were noted to have elevated levels of titanium in the urine t~3~. We have found no evidence in the literature for the utilization of '~STi in radiopharmaceutical or toxicological research, and are suggesting its excellent applicability for such studies. Experimental
All irradiations were carried out at the BNL 60 in. cyclotron. Scandium occurs in nature as 100~o 45Sc and is available from Alpha Inorganics (Beverly, MA) in 99.9% purity * For earlier papers in this series see previous issues of this journal. t Research carried out at Brookhaven National Laboratory under contract with the U.S. Energy Research and Development Administration and supported by its Division of Basic Energy Sciences.
115 A.R.L 29/2
D
in the form of 0.010 in. thick foils at $78.00/in 2 and Sc203 at $12.50/g. An a l u m i n u m ring was used to press the scandium foil into the cavity to the H20-cooled aluminum target block. Alternatively, approximately 150 mg of Sc20 3 was formed into targets by using a hydraulic press and suitable dies. In the case of the Sc20 3 a 0.003 in. Hyvar window was inserted between the a l u m i n u m retaining ring and the pellet. A proton energy of 12.4 MeV was chosen to utilize the optimum section of the 45Sc(p,n)45Ti excitation function, and to stay below the 12.4 MeV threshold of the (p,2n) reaction 114). In principle, the beam current is limited only by the cooling efficiency since both scandium and SC20 3 have melting points higher than that of the a l u m i n u m target holder. Following irradiation, the scandium targets were dissolved in concentrated HC1. Care is required to avoid spattering in the case of the metal. Gentle heating was required in the case of the oxide. One drop of concentrated HNO3 was added to oxidize the titanium to the + 4 state. The excess nitric acid was then destroyed by fuming to dryness, redissolving in concentrated HCI and fuming to dryness again. It is absolutely essential to destroy all the nitric acid as it interferes with the subsequent separation procedure. The 45Ti activity was then dissolved in a m i n i m u m a m o u n t of concentrated HCI and placed on a prewashed ce,umn ( 2 0 m m × 9 0 m m ) of Dowex I-X8, 100/200 mesh. The scandium was washed off the column with concentrated HCI. The presence or absence of scandium in the eluant was checked by addition of a m m o n i a and using the arsenazo III (0.05~o) colorimetric test "s~. The ion exchange procedure eliminates ,~99.2% of the scandium. After the scandium was eluted, the eluting agent was switched to 8 M HC1. The carrier-free 45Ti was recovered in one to two column volumes. The volume of the separated 45Ti was reduced to ~ 0.1 ml. The radiochemical separations were completed in ~ 2 hr from EOB. The radiochemical yield (not optimized) was typically 30~o. A 179#g/cm 2 target of scandium plated on copper was examined at 12.5 MeV. The 45Sc(p,n)45Ti, 45Sc(p,pn)44Sc m and 4aTi(p,n)46V nuclear reactions accounted for 99.8, 0.08 and 0.05% of the activity at the end of bombardment (EOB). The '*'~Sc'~ does not interfere since it is removed in the chemical separation. The simultaneous production of the 4 s v radiocontaminant cannot be avoided, since titanium occurs naturally in the highest purity scandium available. In the case of the Sc203 targets, the 45Ti indicated the presence of nanocurie levels of 56'57'5SCo recoil activities arising from the Hyvar window. The radionuclidic purity of 4~Ti separated from thick targets was >99.95%. The production rate obtained for protons degraded from 12.5 to 10.5 MeV was 9.2 _+ 0.2 mCi/#Ah. The m a x i m u m a m o u n t of 45Ti produced for an irradiation was 81.7 mCi at EOB. The production rate was increased to 17.9 + 0.2 mCi/ pAh at 16.2MeV but the level of 4'*Scm to be removed approached 5%. The 45Ti was used for a preliminary evaluation of selected inorganic and organometallic labeled c o m p o u n d s as potential radiopharmaceuticals. Several complexes were identified and characterized by their behavior on cation and anion exchange resins. The citrate, for example, was strongly adsorbed on an anion resin (Dowex I-X8) but passed through a cation resin (Dowex 50W-X4) without adsorption. Based on their behavior as compared with carrier compounds, and information in the literature, it
Technical notes
116
is concluded that the complexes formed are: citrate, Ti(OH)3(C6HsOT) 2 i1~,~, lactate, Ti(OH)3(C4H306) i 11-1; and ascorbate, Ti(C~,H606) ÷ ~s~. A neutralized material presumed to be '~STiO2 was taken to dryness, and a few drops of 6 M N a O H were added before the solution was titrated to neutrality. We arc uncertain of the chemical nature of the "'dioxide". The material was not eluted from either of the ion exchange resins but remained as a thin band of activity at the tops of the columns. Carrier titanium dioxide is not soluble in neutral solution and the procedure effected would certainly have produced a TiO2 precipitate with carrier titanium. If the material were ionic. it should be soluble and pass through one of the resins. Preliminary studies "9~ in mice were reported to have shown significant differences in the tissue distributions of the 4-~Ti-"dioxide", *STi-citrate and 4STi-lactate. It was reported that the lung uptake at 2hr was 146 ___ 23, 6.2 _+ 0.7 and 9.7 + 1.2%/g, respectively. By comparison the uptake in the spleen at 2 hr was 4.4 __. 2.3, 5.2 + 0.5 and 11.7 +_ 3.4%/g, respectively. Further biological studies with '*STi are justified.
Chemistry Departmen t, Brookhaven National Laboratory, Upton, N Y 11973, U.S.A.
J. C. MERRILL* R . U . LAMBRECHT'~" A.P. WOLE
References 1. LEWES M. B. Nuclear Data Sheets EM, 237-267 (1970). 2. MEZENTSEUN N. V., MEL~DOV^ E. A. and MOGILEVSKAYA, O. YA. In Toxicology of the Rare Metals (Edited by IZRAEL'SON Z. I.), translation from Russian by the Israel Program for Scientific Translations, Jerusalem (1967). 3. TIPTON I. H. In Metal Binding in Medicine (Edited by SEVEN M. J. and JOHNSON L. A.), pp. 27 58. J. B. Lippincott, Philadelphia. 4. SCHROEDERH. A. In Metal Binding in Medicine (Edited by SEVEN M. J. and JOHNSON J. A.), pp. 59-67. J. B. Lippincott. Philadelphia. 5. BERNHEIM F. and BERNHEIM M. L. C. J. biol. Chem. 128, 79 (1939). 6. VOINAR A. 1. Biologicheskaya PoFmikroelementov V organizme Zhivotnykh i Cheloveka (The Biological Role of Trace Elements in Animals and Man). Moskva (1953). 7. MOGILEVSKAYA
8. 9.
10. 11. 12. 13. 14. 15. 16. 17.
O.
YA..
MEL'N1KOVA
E.
A.
and
MEZENTSEVA N. V. Tsvet. Metally 4, 51 (1957). MEL'NIKOVA E. A. Gi~/. Sanit. 5, 27 0958). DEL'VA V. A. Mirroelem. Nerv. Syst., Mater Uses Syrup. pp. 77-83, Bak., 1963 (Publ. 1966). (See Chem. Abstr. 67, 114818M.) KOPITO L. and SWACHMAN H.'Nature. Lond. 202, 501 ( 1964 ). CARROLL K. G. and TULLIS J. L. Nature, Lond. 217(5734), 1172 (1968). DEL'VA V'. A. Trudy donets. (Cos. Inst. med. 23, 17 (1963). (See Chem. Abstr. 66. 103299w.) KV1RIKADZBN. A. Soobsch. Akad. Nauk yruz. SSR 45, 241 (1967). McGEE T., RAO C. L., SANA G. B. and YAEEE L. Nucl. Phys. A150, 11 (1970). ON~SHI H. and BANKS C. V. Analytica chim. Aeta 29, 240 (1963). ZHOLNINA. V. and BOBYRENKO YU. YA. Russ. J. inory. Chem. 16, 194 (1971). ZHOLNIN A. V. and DOLMATOV YU. D. Russ. J. inorg. Chem. 14, 635 (1969).
* Present address: Department of Chemistry, Central Missouri State University, Warrensburg, MO 64093. U.S.A. t To whom enquiries should be addressed.
18. SOMMERL. Colin Czech. chem. Commun. 28, 449 (1963). 19. ATKINS H. L., BRADLEY-MOORE P. R., LAMBRECHT R. M., MERRtLL J. C., PACKER S. and WOLF A. P. J. nucl. Med. 15, 475 (1974).
International Journal of Applied Radiation and Isotopes. 197,~. ~-ot 29 pp 116- 117. IX)20-708X,7S/0201-0116$(I2(R)'0 © Pergamon Press Ltd Printed in Great Britain
The Determination of Parent Radionuclide Activity by Daughter Decay Measurements after Separation of the Two Nuclides with Different Radiochemical Yields IReceired 25 July 1977: in ret'ised form 11 August 1977~ THE DECAY or grow-in of a relatively short-lived daughter nuclide is often followed in order to find the quantity of a relatively long-lived parent present in a mixture Thus if an excess of daughter is present, the decay will deviate from the exponential curve expected from the daughter alone, eventually following the decay of the parent. The general equation of decay is well known:
ABE = [AB/{~'.B -- /.aJ]AAo [exp ( -- 2.4tl exp ( - 28t)] + ,4n0 exp { - ),all
( 11
where Aao is the activity of parent at time 0, ABo is the activity of daughter at time 0, As, is the activity of daughter at time t, 2 A is the decay constant of parent and 2s is the decay constant of daughter. If the half-life of the parent is long compared with that of the daughter and also long enough for its decay to bc ignored, then 2B/(2s - ":~A) ~ 1 and exp(
;.4tt ~ 1
and, applying these approximations, equation [ I ) simplifies to: An, = AAo [1 - exp( - ).st)] + Aso exp( - )-st) (2) or
As, = Aao + [exp(--)-dJ](4BO -- AAOL
(3)
Recently we were attempting to ascertain whether 2'*2Amm (T~ = 152yr) was present with the Z41Am discharged to the environment from the irradiated fuel reprocessing plant at Windscale in Cumbria. This radionuclide decays by electron capture and is thus difficult to detect: the investigation therefore entailed the separation of americium and curium from a sample, followed by measurement of the decay of 242Cm (T~ = 163 days, and daughter of 242Am') to see whether there was indeed any 242Cm supported by a long-lived precursor, in addition to the unsupported 242Cm111" Now the complete separation of americium from curium is difficult, and the purification procedure used resulted in different yields of the two elements; the question then arose: what was the effect of this difference in chemical yield when applied to the measurement of the decay of the daughter in order to obtain the amount of parent present? The question can be answered in the following way: Let the activities of parent and daughter immediately before separation be A'Ao and A'so, respectively, with fractional yields on separation of Y, and Ys, respectively. The activities immediately after separation are thus YaA'A~ and
Cyclotron Isotopes and Radiopharmaceulicals--XXl V.* Titanium-45? (Received 20 M a y 1977)
Introduction
TITANIUM-45 has a half-life of 3.05 hr and decays primarily (85%) by positron emission with EB,~x = 1.04 MeV. Low abundance ( < 1 % ) g a m m a emissions of 0.721, 1.237, 1.411 and 1.665 MeV are also present. The nuclide decays to 4SSc [a stable isotopetl)]. The decay characteristics are appropriate for detection on a positron camera, and the nuclide m a y be suitable for transaxial reconstruction tomography should an appropriate radiopharmaceutical be developed. In many respects 45Ti may be an ideal nuclide for tracing of biological functions and toxicological studies of environmental pollutants. The role of titanium as an essential trace element in the h u m a n body is controversial ~2-4~. Its role in biochemical processes has not been ascertained, although it is found in considerable levels in the body °~. According to BERNHEIM and BERNHEIM15~ titanium is thought to play a role in the oxidation of certain thio-compounds to sulfonic acids. VOINORt6) found that the addition of titanit/m sulfate to the daily diet of blood donors somewhat accelerated the regeneration of serum proteins and raised the erythrocyte count. However, h u m a n studies on titanium and its c o m p o u n d s are few~2'~'sk The presence of the metal in fairly high concentration in the h u m a n brain has been demonstrated 19). The metal is found in the lung of newborns and the a m o u n t increases with age ~3~. Workers exposed to TiO 2 have a high incidence of a lung disease called titantiosis ~2~. Elevated concentrations of titanium were found in patients with cystic fibrosis t~ o~ and in the leukocytes of patients with lymphoblastic leukaemia ~ ) . Titanium has also been found in higher than normal concentrations in cerebral tumors t~-'). Patients with bladder tumors were noted to have elevated levels of titanium in the urine t~3~. We have found no evidence in the literature for the utilization of '~STi in radiopharmaceutical or toxicological research, and are suggesting its excellent applicability for such studies. Experimental
All irradiations were carried out at the BNL 60 in. cyclotron. Scandium occurs in nature as 100~o 45Sc and is available from Alpha Inorganics (Beverly, MA) in 99.9% purity * For earlier papers in this series see previous issues of this journal. t Research carried out at Brookhaven National Laboratory under contract with the U.S. Energy Research and Development Administration and supported by its Division of Basic Energy Sciences.
115 A.R.L 29/2
D
in the form of 0.010 in. thick foils at $78.00/in 2 and Sc203 at $12.50/g. An a l u m i n u m ring was used to press the scandium foil into the cavity to the H20-cooled aluminum target block. Alternatively, approximately 150 mg of Sc20 3 was formed into targets by using a hydraulic press and suitable dies. In the case of the Sc20 3 a 0.003 in. Hyvar window was inserted between the a l u m i n u m retaining ring and the pellet. A proton energy of 12.4 MeV was chosen to utilize the optimum section of the 45Sc(p,n)45Ti excitation function, and to stay below the 12.4 MeV threshold of the (p,2n) reaction 114). In principle, the beam current is limited only by the cooling efficiency since both scandium and SC20 3 have melting points higher than that of the a l u m i n u m target holder. Following irradiation, the scandium targets were dissolved in concentrated HC1. Care is required to avoid spattering in the case of the metal. Gentle heating was required in the case of the oxide. One drop of concentrated HNO3 was added to oxidize the titanium to the + 4 state. The excess nitric acid was then destroyed by fuming to dryness, redissolving in concentrated HCI and fuming to dryness again. It is absolutely essential to destroy all the nitric acid as it interferes with the subsequent separation procedure. The 45Ti activity was then dissolved in a m i n i m u m a m o u n t of concentrated HCI and placed on a prewashed ce,umn ( 2 0 m m × 9 0 m m ) of Dowex I-X8, 100/200 mesh. The scandium was washed off the column with concentrated HCI. The presence or absence of scandium in the eluant was checked by addition of a m m o n i a and using the arsenazo III (0.05~o) colorimetric test "s~. The ion exchange procedure eliminates ,~99.2% of the scandium. After the scandium was eluted, the eluting agent was switched to 8 M HC1. The carrier-free 45Ti was recovered in one to two column volumes. The volume of the separated 45Ti was reduced to ~ 0.1 ml. The radiochemical separations were completed in ~ 2 hr from EOB. The radiochemical yield (not optimized) was typically 30~o. A 179#g/cm 2 target of scandium plated on copper was examined at 12.5 MeV. The 45Sc(p,n)45Ti, 45Sc(p,pn)44Sc m and 4aTi(p,n)46V nuclear reactions accounted for 99.8, 0.08 and 0.05% of the activity at the end of bombardment (EOB). The '*'~Sc'~ does not interfere since it is removed in the chemical separation. The simultaneous production of the 4 s v radiocontaminant cannot be avoided, since titanium occurs naturally in the highest purity scandium available. In the case of the Sc203 targets, the 45Ti indicated the presence of nanocurie levels of 56'57'5SCo recoil activities arising from the Hyvar window. The radionuclidic purity of 4~Ti separated from thick targets was >99.95%. The production rate obtained for protons degraded from 12.5 to 10.5 MeV was 9.2 _+ 0.2 mCi/#Ah. The m a x i m u m a m o u n t of 45Ti produced for an irradiation was 81.7 mCi at EOB. The production rate was increased to 17.9 + 0.2 mCi/ pAh at 16.2MeV but the level of 4'*Scm to be removed approached 5%. The 45Ti was used for a preliminary evaluation of selected inorganic and organometallic labeled c o m p o u n d s as potential radiopharmaceuticals. Several complexes were identified and characterized by their behavior on cation and anion exchange resins. The citrate, for example, was strongly adsorbed on an anion resin (Dowex I-X8) but passed through a cation resin (Dowex 50W-X4) without adsorption. Based on their behavior as compared with carrier compounds, and information in the literature, it
Technical notes
116
is concluded that the complexes formed are: citrate, Ti(OH)3(C6HsOT) 2 i1~,~, lactate, Ti(OH)3(C4H306) i 11-1; and ascorbate, Ti(C~,H606) ÷ ~s~. A neutralized material presumed to be '~STiO2 was taken to dryness, and a few drops of 6 M N a O H were added before the solution was titrated to neutrality. We arc uncertain of the chemical nature of the "'dioxide". The material was not eluted from either of the ion exchange resins but remained as a thin band of activity at the tops of the columns. Carrier titanium dioxide is not soluble in neutral solution and the procedure effected would certainly have produced a TiO2 precipitate with carrier titanium. If the material were ionic. it should be soluble and pass through one of the resins. Preliminary studies "9~ in mice were reported to have shown significant differences in the tissue distributions of the 4-~Ti-"dioxide", *STi-citrate and 4STi-lactate. It was reported that the lung uptake at 2hr was 146 ___ 23, 6.2 _+ 0.7 and 9.7 + 1.2%/g, respectively. By comparison the uptake in the spleen at 2 hr was 4.4 __. 2.3, 5.2 + 0.5 and 11.7 +_ 3.4%/g, respectively. Further biological studies with '*STi are justified.
Chemistry Departmen t, Brookhaven National Laboratory, Upton, N Y 11973, U.S.A.
J. C. MERRILL* R . U . LAMBRECHT'~" A.P. WOLE
References 1. LEWES M. B. Nuclear Data Sheets EM, 237-267 (1970). 2. MEZENTSEUN N. V., MEL~DOV^ E. A. and MOGILEVSKAYA, O. YA. In Toxicology of the Rare Metals (Edited by IZRAEL'SON Z. I.), translation from Russian by the Israel Program for Scientific Translations, Jerusalem (1967). 3. TIPTON I. H. In Metal Binding in Medicine (Edited by SEVEN M. J. and JOHNSON L. A.), pp. 27 58. J. B. Lippincott, Philadelphia. 4. SCHROEDERH. A. In Metal Binding in Medicine (Edited by SEVEN M. J. and JOHNSON J. A.), pp. 59-67. J. B. Lippincott. Philadelphia. 5. BERNHEIM F. and BERNHEIM M. L. C. J. biol. Chem. 128, 79 (1939). 6. VOINAR A. 1. Biologicheskaya PoFmikroelementov V organizme Zhivotnykh i Cheloveka (The Biological Role of Trace Elements in Animals and Man). Moskva (1953). 7. MOGILEVSKAYA
8. 9.
10. 11. 12. 13. 14. 15. 16. 17.
O.
YA..
MEL'N1KOVA
E.
A.
and
MEZENTSEVA N. V. Tsvet. Metally 4, 51 (1957). MEL'NIKOVA E. A. Gi~/. Sanit. 5, 27 0958). DEL'VA V. A. Mirroelem. Nerv. Syst., Mater Uses Syrup. pp. 77-83, Bak., 1963 (Publ. 1966). (See Chem. Abstr. 67, 114818M.) KOPITO L. and SWACHMAN H.'Nature. Lond. 202, 501 ( 1964 ). CARROLL K. G. and TULLIS J. L. Nature, Lond. 217(5734), 1172 (1968). DEL'VA V'. A. Trudy donets. (Cos. Inst. med. 23, 17 (1963). (See Chem. Abstr. 66. 103299w.) KV1RIKADZBN. A. Soobsch. Akad. Nauk yruz. SSR 45, 241 (1967). McGEE T., RAO C. L., SANA G. B. and YAEEE L. Nucl. Phys. A150, 11 (1970). ON~SHI H. and BANKS C. V. Analytica chim. Aeta 29, 240 (1963). ZHOLNINA. V. and BOBYRENKO YU. YA. Russ. J. inory. Chem. 16, 194 (1971). ZHOLNIN A. V. and DOLMATOV YU. D. Russ. J. inorg. Chem. 14, 635 (1969).
* Present address: Department of Chemistry, Central Missouri State University, Warrensburg, MO 64093. U.S.A. t To whom enquiries should be addressed.
18. SOMMERL. Colin Czech. chem. Commun. 28, 449 (1963). 19. ATKINS H. L., BRADLEY-MOORE P. R., LAMBRECHT R. M., MERRtLL J. C., PACKER S. and WOLF A. P. J. nucl. Med. 15, 475 (1974).
International Journal of Applied Radiation and Isotopes. 197,~. ~-ot 29 pp 116- 117. IX)20-708X,7S/0201-0116$(I2(R)'0 © Pergamon Press Ltd Printed in Great Britain
The Determination of Parent Radionuclide Activity by Daughter Decay Measurements after Separation of the Two Nuclides with Different Radiochemical Yields IReceired 25 July 1977: in ret'ised form 11 August 1977~ THE DECAY or grow-in of a relatively short-lived daughter nuclide is often followed in order to find the quantity of a relatively long-lived parent present in a mixture Thus if an excess of daughter is present, the decay will deviate from the exponential curve expected from the daughter alone, eventually following the decay of the parent. The general equation of decay is well known:
ABE = [AB/{~'.B -- /.aJ]AAo [exp ( -- 2.4tl exp ( - 28t)] + ,4n0 exp { - ),all
( 11
where Aao is the activity of parent at time 0, ABo is the activity of daughter at time 0, As, is the activity of daughter at time t, 2 A is the decay constant of parent and 2s is the decay constant of daughter. If the half-life of the parent is long compared with that of the daughter and also long enough for its decay to bc ignored, then 2B/(2s - ":~A) ~ 1 and exp(
;.4tt ~ 1
and, applying these approximations, equation [ I ) simplifies to: An, = AAo [1 - exp( - ).st)] + Aso exp( - )-st) (2) or
As, = Aao + [exp(--)-dJ](4BO -- AAOL
(3)
Recently we were attempting to ascertain whether 2'*2Amm (T~ = 152yr) was present with the Z41Am discharged to the environment from the irradiated fuel reprocessing plant at Windscale in Cumbria. This radionuclide decays by electron capture and is thus difficult to detect: the investigation therefore entailed the separation of americium and curium from a sample, followed by measurement of the decay of 242Cm (T~ = 163 days, and daughter of 242Am') to see whether there was indeed any 242Cm supported by a long-lived precursor, in addition to the unsupported 242Cm111" Now the complete separation of americium from curium is difficult, and the purification procedure used resulted in different yields of the two elements; the question then arose: what was the effect of this difference in chemical yield when applied to the measurement of the decay of the daughter in order to obtain the amount of parent present? The question can be answered in the following way: Let the activities of parent and daughter immediately before separation be A'Ao and A'so, respectively, with fractional yields on separation of Y, and Ys, respectively. The activities immediately after separation are thus YaA'A~ and