Sodium-24 (Na1124) is used to study the circulatory system and to treat chronic

Question

Sodium-24 (Na1124) is used to study the circulatory system and to treat chronic leukemia, and has a half-life of 14.959 hours. It is administered in the form of saline (NaCl) solution, with a therapeutic dosage of 180 Ci/kg body weight.

a.How many milliliters of a 7.50 mCi/mL solution are needed to treat a 110.0 kg adult?

b. Sometime after delivering the correct dosage for the patient in part a, a nurse pulls a blood sample and finds the Sodium-24 level to be 85.7 Ci/kg body weight. How many hours after the administration of the dose did the nurse pull the blood sample?

Explanation / Answer

therapeutic dosage= 160uCI/kg

1 kg requires 180uCi

110 kg requires 110*180=19800 uCI=19800*10-6 CI

solution concentration= 7.50mCI/ml =7.5*10-3CI/ml

ml requires= 19800*10-6/7.5*10-3 ml=2.64ml

b) from C= Co*e(-Kt)

where C0= 180uCI/kg body weight and C= 85.7 uCI/kg body weight

K= rate constant =0.693/half ilfe= 0.693/14.959=0.0463/hr

C/CO= e(-Kt)

85.7/180 = e(-Kt) = e(-0.0463*t)

0.476= e(-0.463t)

taking ln, the equation becomes

ln(0.476)= -0.463t

t=1.59 hrs

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