Chapter 32, Problem 6PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# The activities of 131I and 123I used in thyroid scans are given in Table 32.1the 50 and 70 μCi, respectively. Find and compare the masses of 13lI and 231I in such scans, given their respective half−lives are 8.04 d and 13.2 h. The masses are so small than the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body.

To determine

The comparison between the masses of I131 and I123.

Explanation

Given info:

The activity of I131 is

â€ƒâ€ƒA=0.05â€‰mÂ·Ci

The half-life of I131 is

â€ƒâ€ƒT1/2=8.04day=8.04Ã—24Ã—3600sec

The activity of I123 is

â€ƒâ€ƒA=0.07â€‰mÂ·Ci

The half-life of I123 is

â€ƒâ€ƒT1/2=13.2h=13.2Ã—3600sec

Formula used:

The mass can be found as

â€ƒâ€ƒm=NNaÃ—molarâ€‰mass

Calculation:

Mass of I131

The activity

â€ƒâ€ƒA=0.05â€‰â€‰mÂ·Ci=0.05Ã—3.70Ã—107BqA=1.85Ã—106Bq

Activity is defined as

â€ƒâ€ƒA=Nln2T 1 2N=AT1/2ln2

Substituting the values

â€ƒâ€ƒN=(1.85Ã—106Bq)Ã—8.04Ã—24Ã—3600secln2N=1.85Ã—1012â€‰atoms

Substituting all values, the mass of mI131 is

â€ƒâ€ƒmI131=1.85Ã—1012â€‰atoms6.02Ã—1023â€‰atomsÃ—131â€‰gmI131=4.03Ã—10âˆ’10g

Mass of I123

The activity

â€ƒâ€ƒA=0.07â€‰â€‰mÂ·Ci=0

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