Saved Bookmarks
| 1. |
I^(131)is an isotope of iodine that p decays to an isotope of xenon with a half-life of 8 days. A small amount of a serum labelled with I^131 is injected into the blood of a person. The activity of the amount of I^131 injected was2.4 xx 10^5 becquerel (Bq). It is known th a t the injected serum will get distributed uniformly in the blood stream in less th an h alf an hour. After 11.5 hours, 2.5 ml of blood is drawn from person’s body, and gives an activity of 115 Bq. The total volume of blood in the person’s body, in litres, is approximately (you m ay usee^(x) ~~ 1+x for |x| lt lt 1 and in 2 ~~ 0.7). |
|
Answer» Solution :The `BETA`-decay reaction is as follows:`I^(131) to Xe^(131) + beta` Given that the initial activity of the`I^(131)` , `A_(0)=2.4 xx 10^(4)` Bq Let the decay constant for `I^131` be A and the volume of the blood in the person’s body be V. The activity of the 2.5 ml of blood at time t, A = 115 Bq Thus, activity of 1 ml of blood, `115/2.5 =46` Bq thus, the activity of volume V of the blood, `A = 46 Bq` `A =A_(0)e^(-lambdat)` `46 V = 2.4 xx 10^(5)e^(-lambdat)` `lambda =(ln2)/T =(ln 2)/(8 "days") =(ln 2)/(8 xx 24)hr^(-1)` `46 V = 2.4 xx 10^(5) xx e^(-(0.7 xx 11.5)/(8 xx 24))` `46 V = 2.4 xx 10^(5) xx 0.9583` `V=(2.4 xx 10^(5) xx 0.9583)/46` =5 litres. |
|