Radioactive iodine is used frequently in biological studies. A radiation biologi
ID: 939287 • Letter: R
Question
Radioactive iodine is used frequently in biological studies. A radiation biologist studies the rate of decomposition of this substance and obtains the following data:
t (days)....... 0 ...........4.0 ..........8.0 ..........12.0 ...........16.0
Mass (µg) 12.0........ 8.48.......... 6.0 ...........4.24 ...........3.0
(a) Assume this is a first order reaction, determine the rate constant, including appropriate units. (b) How many micrograms will be left after 32 days? (c) How many days will it take for the sample size to decrease to 1.2 µg?
Explanation / Answer
Apply Half life equation
A = A0*(1/2)^(t/HL)
A0 = 12 micrograms
1/2 of A0 = 12/2 = 6 micrograms, when this happens, t = 8 days
this must be the half life so
HL = 8 days
then
a)
for a first order equation, the half life is given as:
t1/2 = ln(2)/k
solve for k
k = ln(2)/(8) = 0.08664 1/day
b)
after t = 32, find mass
A = (A0)(1/2)^(t/HL)
A = (12)(1/2)^(32/8) = 0.75 micrograms left after 32 days
c)
time require dfor A final = 1.2 micrograms
A = (A0)(1/2)^(t/HL)
1.2 = 12*(1/2)^(t/8)
solve for t
0.1 = (0.5)^(t/8)
t = 26.57 days
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