Practice Problem B
How much 206-Pb will be in a rock sample that is 1.3x10^8 years old and that contains 3.25mg of 238-U?
The correct answer is supposed to be 5.7 x 10^-2 mg. Can anyone help explain how to get this answer??
How much 206-Pb will be in a rock sample that is 1.3x10^8 years old and that contains 3.25mg of 238-U?
The correct answer is supposed to be 5.7 x 10^-2 mg. Can anyone help explain how to get this answer??
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The half-life of U-238 is 4.468 x 10^9 yr. I found that value here:
https://en.wikipedia.org/wiki/Isotopes_o…
1.3 x 10^8 yr divided by 4.468 x 10^9 yr = 0.029098 (this is how many half-lives have elapsed)
(1/2)^0.029098 = 0.9800 (this is the decimal amount of U-238 remaining)
3.25 mg is to 0.98 as x is to 1
x = 3.3163 mg (this is the amount of U-235 at the start of the decay)
3.3163 - 3.25 = 0.0663 mg (of U-235 that decayed)
0.0000663 g / 238.05 g/mol = 2.78513 x 10^-7 mol of U-238
This means 2.78513 x 10^-7 mol of Pb-206 was formed.
2.78513 x 10^-7 mol times 205.97 g/mol = 0.0000573653 g
to two sig figs and using mg, this is 0.057 mg
https://en.wikipedia.org/wiki/Isotopes_o…
1.3 x 10^8 yr divided by 4.468 x 10^9 yr = 0.029098 (this is how many half-lives have elapsed)
(1/2)^0.029098 = 0.9800 (this is the decimal amount of U-238 remaining)
3.25 mg is to 0.98 as x is to 1
x = 3.3163 mg (this is the amount of U-235 at the start of the decay)
3.3163 - 3.25 = 0.0663 mg (of U-235 that decayed)
0.0000663 g / 238.05 g/mol = 2.78513 x 10^-7 mol of U-238
This means 2.78513 x 10^-7 mol of Pb-206 was formed.
2.78513 x 10^-7 mol times 205.97 g/mol = 0.0000573653 g
to two sig figs and using mg, this is 0.057 mg