1. in our study of planet building, we have said that the planets and most of th
ID: 289598 • Letter: 1
Question
1. in our study of planet building, we have said that the planets and most of the large bodies in the solar system are differentiated. First of all, what does it mean to be differentiated? Second, how and why do the bodies become differentiated?
2. Suppose we have found an analyzed a meteorite. Our results show that for every 1000 atoms of potassium-40 that would have been originally present in the meteorite, only 125 have not yet decayed. We know that the half-life of potassium-40 is 1.3 billion years. Calculate the age of the meteorite. When the meteorite reaches twice its current age, how many potassium-40 atoms will still be present per 1000 that were originally present in the meteorite?
Explanation / Answer
2. By analyzing the meteorite, it has been found that for every 100 atoms of potassium-40 that would have been originally present in the meteorite, only 125 have not yet decayed.
Now, by the definition of Half-life of radio-active elements, after one half-life, there will be just half the number of atoms present that that was there at the beginning.
So, if there were 1000 atoms present at the beginning.
after one half-life there will be, 500 undecayed atoms in the system,
and after two half-lives, there will be, 250 undecayed atoms in the system,
and after three half-lives, there will be, 125 undecayed atoms in the system.
So, the potassium-40 atoms must have undergone 3 half-lives.
We know that the half-life of potassium-40 is 1.3 billion years,
Therefore the age of the meteorite is 3*1.3 or 3.9 billion years.
When the meteorite reaches twice its current age, there must be 6 half-lives gone.
So after 6 half-lives, there will be (1000/2^6) or (1000/64) ~ 16 potassium-40 atoms will still be present per 1000 that were originally present in the meteorite.
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