Iridium-192 is one radioisotope used in brachytherapy, in which a radioactive so

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. Sample remaining (%) 100 90 . 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (days)

Explanation / Answer

Part a

Initial mass = 5.75 g

From the graph after 55 days, sample remains = 60%

After 55 days

Sample remains = 5.75*0.6 = 3.45 g

Part b

Half life is when the 50% of the sample remains of its initial value.

From the graph

50% sample remains after 75 days

Half life = 75 days.

Now we will prove theoretically

Ln(m(t) / m(to)) = - x t

= - ln(mo / mi) / t
= - ln(3.45 / 5.75) / 55
= 9.28 x 10^-3 day^-1

T½ = ln(2) /
T½ = ln(2) / 9.28 x 10^-3
T½ = 74.69 days = 75 days

Part C

One fourth decay means 1-(1/4) = 0.75 = 75% of the sample remains.

From the graph

75% of the sample remains after 30 days.

Now we will do theoretically to prove.

mf / mi = 0.75
ln (mf / mi) = - x t
t = - ln(mf / mi) /
t = - ln(0.75) / 9.28 x 10^-3
t = 31 days

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