Map Iridium-192 is one radioisotope used in brachytherapy, in which a radioactiv

Question

Map 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 tunor 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 40 50 40 30 @ 10 0020 30 40 0 20 30 40 eo 70 so 80 100 110 20130 140 150 0170 180180 200 Time (days) a) If the initial sample is 4.75 g, what mass of the original iridium-192 remains after 65 days? Number continued below @check Answer. O Next Exit Hint

Explanation / Answer

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With the aid of the computer you can answer the questions rapidly.

a) Put your cursor on 65 and go in a straight line to the graph: Get the number of the percentage of Iridium remaining. It should be close to 55%. If the initial sample is 4.75 g you can calculate:

Mass Ir-192 remaining = 4.75 g x 55/100 = 2.613 g

b) Halftime of a radioisotope is, by definition, is the time required for one half of a given number of atoms to decay. The half-life, t1/2 is also related to the disintegration constant, l (lamda), by the relation:

t1/2 = 0.693/l

It can also be determined graphically by looking at the number of days it take to disintegrate half of the number of atoms or 50% of the sample. So you go to 50% in the y axis and go again straight to the graph and see what number of days it corresponds. From my point of view it seems close to 70 days

c) Decay kinetics for a radioactive isotope is a first order process. It follows the First-Order Rate Equation: ln(Nt/N0) = -lt

The parameters are: Nt is the number of atoms after time = t; N0 is the number of atoms at time = 0; l(lamda) is the disintegration constant and t = time

In this equation, the units of measure for Nt and N0 can be in grams, atoms, or moles. It does not matter as long as they are like measures. The units of measure for time are dependent upon the unit of measure for the rate constant. The ratio of "Nt/N0" gives the percentage activity as compared to the activity at time zero. The disintegration constant can be determined graphically plotting lnNt = lnN0 - lt. –l will be the slope of the straight line.

However you have a graph where you can find the data with your cursor so estimate whta percentage of sample remains after the decay of 1/3. If 1/3 have decay then 2/3 remains. The percentage remaining is:

% = 100 x 2/3 = 66.6%

Then go to the graph look up 66.6% go straight to the curve and find the number of days. From my point of view is something around 45 days. If you don’t have that percentage in the graph and you need to calculate precisely then draw the graph selecting several points from the original curve plotting lnNt versus t. The slope is l and you can calculate the number of days (t) using 2/3 of the mass: 4.75 g x 2/3 = 3.17 g

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