The Kingdom of Chemithia- Part 11

Chemistry Level 4

When you identify the salt, you go up to King Antimony. He is shocked to find out your result. It means that the Alkemians are taking Selene to the heart of Alkemia, in the region known as the Oganesson Traps! You need to start moving immediately in order to rescue Selene; the Oganesson Traps are known for having a very rich supply of radioactive \(_{232}Th^{90}\)! The Alkemians have effectively set a trap: go rescue Selene from there and possibly give up the uranium supply in return, or the Alkemians can just leave her there to die a slow and painful death, constantly exposed to the radiations, and kept as prisoner.

Of course, King Antimony will allow neither of these to happen: Uranium is far too important as a resource to Chemithia, and he will never let Selene die. But before going to the Oganesson Traps, you advise King Antimony to let you do a bit of research before leaving.

So you enter the royal library and begin reading about the Oganesson Traps. It was the site of the very first nuclear reactor attempt by the Alkemians. However it failed and the entire plant underwent a small explosion. The Thorium from the reactor was sent into the ground and the entire area was abandoned. As you are reading, the town museum owner enters the library and sees you reading about the Oganesson traps.

He says that he has received a fossil from an archaelogist friend of his, who unearthed it in the Oganesson Traps. Because of the explosion, the fossil has a higher concentration of \(C^{14}\). His archaeologist friend determined the age of the fossil to be \(T_1\), and the concentration of \(C^{14}\) to be \(C_1\). The museum curator would like you to date another exactly identical fossil (no, not like that!) and compare the 2 ages to study the effect of the radiation on the Oganesson fossil. Though you would normally be hesitant to take up such a job in the midst of the Alkemian crisis, you feel it would be helpful for determining precisely how dangerous the Oganesson Traps really are.

You go back to your lab, where the concentration of \(C^{14}\) is normal, and find the age of the fossil to be \(T_2\), and the concentration of the \(C^{14}\) is \(C_2\). Then which of the following is true?

  1. The fossil appears older in your lab than in the Oganesson Traps.
  2. The fossil appears older in the Oganesson Traps than in your lab.
  3. \(T_1/T_2=C_1/C_2\)
  4. \(T_1-T_2=(1/λ)*ln(C_1/C_2)\)
  5. The age of the fossils will be the same.

Input your answer as the sum of the correct option numbers.

[Note: Assume the 2 fossils are exactly the same as in they have the same structure, shape, time of death in the prehistoric era, etc.]

This question is part of my set Tales of Chemithia! Give it a try; it's a story woven together by Chemistry problems!


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