How much time must elapse before the activity of the source is reduced by 45%?What is the effective decay constant?

Applied Nuclear Physics Homework 9

1. Determine the effective half-life and the effective decay constant for each pair of physical and biological half-lives.
(a) t1/2(phy) = 2.40 minutes and t1/2(bio) = 4.50 minutes;
(b) t1/2(phy) = 18.3 hours and t1/2(bio) = 5.73 hours;
(c) t1/2(phy) = 5.30 days and t1/2(bio) = 14.5 days.

2. What is the average life of a source if its half-life is
(a) 2.80 x 10-6 second?
(b) 16.2 minutes?
(c) 370 hours?
(d) 9.00 x 1010 years?

3. Iodine-131 has a physical half-life of 8.07 days. When in the thyroid, it has a biological half-life of 14 days.
(a) What is the effective half-life of iodine-131 in the thyroid?
(b) What is the corresponding effective decay constant?
(c) What is the corresponding average lifetime?

4. A 5.00 microcurie sample of iodine-131 is placed into living tissue. The physical half-life is 8.07 days, and the biological half-life is 10.2 days in this tissue.
(a) What is the effective half-life?
(b) What is the effective decay constant?
(c) How much time must elapse before the activity of the source is reduced by 45%?

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