Difference between revisions of "Problem set 2"
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− | = Mother | + | = Mother daughter Relations and Equilibrium<br> = |
− | ====== | + | ====== Return to [[Problem Solving Sets]] ====== |
− | + | <br> | |
− | <br> | + | <br> |
− | + | '''1:''' | |
− | + | One kg of fresh and dry thorium nitrate, Th(NO<sub>3</sub>)<sub>4</sub>, is produced from a natural occurring thorium containing ore.<br> | |
− | #Calculate the rate <sup>232</sup>Th and <sup>228</sup>Th disintegrates | + | #Calculate the rate <sup>232</sup>Th and <sup>228</sup>Th disintegrates, and explain why the rate of disintegration is approximately equal for both of the thorium isotopes.<br> |
− | + | #What is the weight of <sup>228</sup>Th in the thorium nitrate?<br> | |
− | #What is the weight of <sup>228</sup>Th in the thorium nitrate?<br> | + | #<sup>228</sup>Ra separated from a one year old thorium nitrate can be placed on a column to make an isotope generator. The chemical yield for this process is 90%. How much amount of thorium nitrate is required to make the column, if <sup>228</sup>Ra disintegrates with 10 000Bq?<br> |
− | #<sup>228</sup>Ra separated from a one year old thorium nitrate can be placed on a column to make an isotope generator. The chemical yield for this process is 90%. How much amount of thorium nitrate is required to make the column, if <sup>228</sup>Ra disintegrates with 10 000Bq?<br> | + | #At which rate will <sup>224</sup>Ra disintegrate 3 days after the column is made?<br> |
− | #At which rate will <sup>224</sup>Ra disintegrate 3 days after the column is made?<br> | ||
#Are there any other radionuclides present at a noteworthy amount (more than 100Bq)?<br> | #Are there any other radionuclides present at a noteworthy amount (more than 100Bq)?<br> | ||
− | '''<br>''' | + | '''<br>''' |
− | '''2:''' | + | '''2:''' |
− | #Which radionuclides are present at t=0?<br> | + | One gram of natural uranium is purified to contain no other elements than uranium at the time t equals 0.<br> |
− | #What are their respective rates of disintegration?<br> | + | |
− | #Which radionuclides are present at t=25,5h?<br> | + | #Which radionuclides are present at t=0?<br> |
− | #What are their respective rates of disintegration?<br> | + | #What are their respective rates of disintegration?<br> |
− | #Which radionuclides are present at t=24d?<br> | + | #Which radionuclides are present at t=25,5h?<br> |
− | #What are their respective rates of disintegration?<br> | + | #What are their respective rates of disintegration?<br> |
− | #Which radionuclides are present at t=1.0a?<br> | + | #Which radionuclides are present at t=24d?<br> |
− | #What are their respective rates of disintegration?<br> | + | #What are their respective rates of disintegration?<br> |
− | #Which radionuclides are present at t=10.0a?<br> | + | #Which radionuclides are present at t=1.0a?<br> |
+ | #What are their respective rates of disintegration?<br> | ||
+ | #Which radionuclides are present at t=10.0a?<br> | ||
#What are their respective rates of disintegration?<br><br> | #What are their respective rates of disintegration?<br><br> | ||
− | '''3:''' A given amount of alum shale contains 10 grams naturally occurring uranium.<br> | + | '''3:''' |
+ | |||
+ | A given amount of alum shale contains 10 grams naturally occurring uranium.<br> | ||
− | #What amounts of radium in Bq and grams does the same alum shale contain?<br> | + | #What amounts of radium in Bq and grams does the same alum shale contain?<br> |
− | #Which amount of <sup>210</sup>Pb is present?<br> | + | #Which amount of <sup>210</sup>Pb is present?<br> |
#<sup>210</sup>Pb is a weak beta emitter, but is still very toxic in large amounts. Why is it so?<br> | #<sup>210</sup>Pb is a weak beta emitter, but is still very toxic in large amounts. Why is it so?<br> | ||
− | <br> | + | <br> |
+ | |||
+ | '''4:''' | ||
− | + | Some radionuclides have a major application in medicine. For practical reasons it is advantageous if these can be produced with the help of an isotope generator.<br> | |
− | #Explain how an isotope generator may impact practical conditions.<br> | + | #Explain how an isotope generator may impact practical conditions.<br> |
− | #Which of the following medical radionuclides can be produced by an isotope generator? <sup>67</sup>Ga, <sup>68</sup>Ga,<sup>6</sup><sup>4</sup>Cu, <sup>82</sup>Br, <sup>89</sup>Sr, <sup>90</sup>Y, <sup>123</sup>I, <sup>131</sup>I, <sup>177</sup>Lu,<sup>201</sup>Tl, <sup>211</sup>At, <sup>212</sup>Pb, <sup>211</sup>At, <sup>223</sup>Ra.<br> | + | #Which of the following medical radionuclides can be produced by an isotope generator? <sup>67</sup>Ga, <sup>68</sup>Ga,<sup>6</sup><sup>4</sup>Cu, <sup>82</sup>Br, <sup>89</sup>Sr, <sup>90</sup>Y, <sup>123</sup>I, <sup>131</sup>I, <sup>177</sup>Lu,<sup>201</sup>Tl, <sup>211</sup>At, <sup>212</sup>Pb, <sup>211</sup>At, <sup>223</sup>Ra.<br> |
− | #In heart examination <sup>201</sup>Tl is used in amounts of 100MBq by intravenously injection of the radionuclide. Which chemical amounts does this equal?<br> | + | #In heart examination <sup>201</sup>Tl is used in amounts of 100MBq by intravenously injection of the radionuclide. Which chemical amounts does this equal?<br> |
#Thallium is a potent rat toxin, why do patients survive these examinations?<br><br> | #Thallium is a potent rat toxin, why do patients survive these examinations?<br><br> | ||
− | '''5:''' A daughter nuclide is eluted from a 100 MBq <sup>44</sup>Ti source in a column.<br> | + | '''5:''' |
+ | |||
+ | A daughter nuclide is eluted from a 100 MBq <sup>44</sup>Ti source in a column.<br> | ||
− | #How long does it take before 50 MBq of the daughter can be eluted from the system?<br> | + | #How long does it take before 50 MBq of the daughter can be eluted from the system?<br> |
#At this point, how much does the respective amounts of nuclides weight?<br> | #At this point, how much does the respective amounts of nuclides weight?<br> | ||
− | <br> | + | <br> |
+ | |||
+ | '''6:''' | ||
+ | |||
+ | Minerals containing thorium emits strong gamma radiation, without any of the involved thorium isotopes emitting gamma.<br> | ||
− | + | #Explain where the gamma radiation is coming from.<br> | |
+ | #Which thorium isotopes exists in natural thorium, and what is the relation between them?<br> | ||
+ | #As a rule of thumb, it is said equilibrium is achieved after 10 halfe-lives. How much time must pass before equilibrium is reached throughout the entire chain of natural occurring thorium and uranium?<br> | ||
− | + | <br> | |
− | |||
− | |||
− | + | '''7:''' | |
− | + | 100 grams of fresh metallic thorium is prepared from naturally occurring thorium containing minerals.<br> | |
− | #What is the rate of disintegration?<br> | + | #What is the rate of disintegration?<br> |
− | #How many grams of <sup>228</sup>Th are present?<br> | + | #How many grams of <sup>228</sup>Th are present?<br> |
− | #How many grams of <sup>229</sup>Th are present?<br> | + | #How many grams of <sup>229</sup>Th are present?<br> |
#What is the total activity of the metallic thorium 7.2 days after it was made, and how is the branching ratio between alpha and beta radiation?<br> | #What is the total activity of the metallic thorium 7.2 days after it was made, and how is the branching ratio between alpha and beta radiation?<br> | ||
− | <br> | + | <br> |
+ | |||
+ | '''8:''' | ||
− | + | A source of 10 000 Bq from the very long lived <sup>194</sup>Hg is used to produce <sup>194</sup>Au. Assume 100% efficiency in the production process.<br> | |
− | #How long does it take until 1000 Bq of the daughter can be extracted from the mother?<br> | + | #How long does it take until 1000 Bq of the daughter can be extracted from the mother?<br> |
#How long does it take until 7500 Bq can be extracted?<br> | #How long does it take until 7500 Bq can be extracted?<br> | ||
− | <br> | + | <br> |
+ | |||
+ | '''9:''' | ||
− | + | The radionuclide <sup>211</sup>At is planned to be used for medical purposes. It has a branching of 58% EC and 42% α.<br> | |
− | #Explain why you get a long lived daughter from one of these branches.<br> | + | #Explain why you get a long lived daughter from one of these branches.<br> |
− | #What is the weight of At in a 50 MBq <sup>211</sup>At sample?<br> | + | #What is the weight of At in a 50 MBq <sup>211</sup>At sample?<br> |
− | #What is the rate of disintegration one week after the sample was made?<br> | + | #What is the rate of disintegration one week after the sample was made?<br><br> |
− | <br> | + | <br> |
− | <br> | + | <br> |
− | <br> | + | <br> |
− | + | [[Category:Unsolved_Problems]][[Category:Bachelor]] |
Latest revision as of 10:01, 9 July 2012
Mother daughter Relations and Equilibrium
Return to Problem Solving Sets
1:
One kg of fresh and dry thorium nitrate, Th(NO3)4, is produced from a natural occurring thorium containing ore.
- Calculate the rate 232Th and 228Th disintegrates, and explain why the rate of disintegration is approximately equal for both of the thorium isotopes.
- What is the weight of 228Th in the thorium nitrate?
- 228Ra separated from a one year old thorium nitrate can be placed on a column to make an isotope generator. The chemical yield for this process is 90%. How much amount of thorium nitrate is required to make the column, if 228Ra disintegrates with 10 000Bq?
- At which rate will 224Ra disintegrate 3 days after the column is made?
- Are there any other radionuclides present at a noteworthy amount (more than 100Bq)?
2:
One gram of natural uranium is purified to contain no other elements than uranium at the time t equals 0.
- Which radionuclides are present at t=0?
- What are their respective rates of disintegration?
- Which radionuclides are present at t=25,5h?
- What are their respective rates of disintegration?
- Which radionuclides are present at t=24d?
- What are their respective rates of disintegration?
- Which radionuclides are present at t=1.0a?
- What are their respective rates of disintegration?
- Which radionuclides are present at t=10.0a?
- What are their respective rates of disintegration?
3:
A given amount of alum shale contains 10 grams naturally occurring uranium.
- What amounts of radium in Bq and grams does the same alum shale contain?
- Which amount of 210Pb is present?
- 210Pb is a weak beta emitter, but is still very toxic in large amounts. Why is it so?
4:
Some radionuclides have a major application in medicine. For practical reasons it is advantageous if these can be produced with the help of an isotope generator.
- Explain how an isotope generator may impact practical conditions.
- Which of the following medical radionuclides can be produced by an isotope generator? 67Ga, 68Ga,64Cu, 82Br, 89Sr, 90Y, 123I, 131I, 177Lu,201Tl, 211At, 212Pb, 211At, 223Ra.
- In heart examination 201Tl is used in amounts of 100MBq by intravenously injection of the radionuclide. Which chemical amounts does this equal?
- Thallium is a potent rat toxin, why do patients survive these examinations?
5:
A daughter nuclide is eluted from a 100 MBq 44Ti source in a column.
- How long does it take before 50 MBq of the daughter can be eluted from the system?
- At this point, how much does the respective amounts of nuclides weight?
6:
Minerals containing thorium emits strong gamma radiation, without any of the involved thorium isotopes emitting gamma.
- Explain where the gamma radiation is coming from.
- Which thorium isotopes exists in natural thorium, and what is the relation between them?
- As a rule of thumb, it is said equilibrium is achieved after 10 halfe-lives. How much time must pass before equilibrium is reached throughout the entire chain of natural occurring thorium and uranium?
7:
100 grams of fresh metallic thorium is prepared from naturally occurring thorium containing minerals.
- What is the rate of disintegration?
- How many grams of 228Th are present?
- How many grams of 229Th are present?
- What is the total activity of the metallic thorium 7.2 days after it was made, and how is the branching ratio between alpha and beta radiation?
8:
A source of 10 000 Bq from the very long lived 194Hg is used to produce 194Au. Assume 100% efficiency in the production process.
- How long does it take until 1000 Bq of the daughter can be extracted from the mother?
- How long does it take until 7500 Bq can be extracted?
9:
The radionuclide 211At is planned to be used for medical purposes. It has a branching of 58% EC and 42% α.
- Explain why you get a long lived daughter from one of these branches.
- What is the weight of At in a 50 MBq 211At sample?
- What is the rate of disintegration one week after the sample was made?