Iridium-192 is one radioisotope used in brachytherapy, in which a radioactive so
ID: 1073293 • Letter: I
Question
Iridium-192 is one radioisotope used in brachytherapy, in which a radioactive source is placed inside a patient's body to treat cancer. Brachytherapy allows the use of a higher than normal dose to be placed near the tumor while lowering the risk of damage to healthy tissue. Iridium-192 is often used in the head or breast. Answer the following three questions (a, b, and c) based on the radioactive decay curve of iridium-192, shown below. Click on the graph and move the mouse over a point to get values for that point.
A) a) If the initial sample is 7.50 g, what mass of the original iridium-192 remains after 105 days?
B? b) Estimate the half-life of the radioisotope.
C) c) How many days would it take for three-fourths of the sample to decay?
Explanation / Answer
a)
A0 = 7.5 g
HL = 73.83 days
t = 105 days
then
Apply half life equation
A = A0*(1/2)^(t/HL)
A = 7.5*(1/2)^(105/73.83)
A = 2.79859 g left
b)
HL = 73.83 days
c)
days required for 3/4 to decay
so
Afinal = 3/4*A0
so
Af = A0*(1/2)^(t/HL)
3/4*A0 = A0*(1/2)^(t/73.83)
0.74 = (1/2)^(t/73.83)
ln(0.75)/ln(0.5) = t/73.83
t = 73.83*0.41503
t = 30.64 days
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