AST 100 Home work question help

Dmagrino

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10 years ago

You are analyzing Moon rocks that contain small amounts of uranium-238, which decays into lead with a half-life of about 4.5 billion years.

In a rock from the lunar highlands, you determine that 50% of the original uranium-238 remains, while the other 50% has decayed into lead. How old is the rock?

In a rock from the lunar maria, you find that 56% of the original uranium-238 remains, while the other 44% has decayed into lead. Is this rock older or younger than the highlands rock?

By how much?

----- I know the first answer to the problem is 4.5 billion years
And its younger but i can't get the correct answer ... its = to billion years

Thank you guys in advanced

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padre

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10 years ago

A question like this was posted a while ago, but with these differences

Quote

In a rock from the lunar highlands, you determine that 55% of the original uranium-238 remains, while the other 45% has decayed into lead. How old is the rock?

The solution (just change your numbers with the ones shown below)

You know the half-life = 4.5x10^9 years.

You should also know the equation for continuous decay:
Psubt = Psub0*e^(-k/t)

You already know Psubt is 0.55 and Psub0 is 1 (because 100% of the uranium was present to begin with). You also know that k = 4.5x10^9.

Plug this all in and you get:

0.55 = e^(-4.5x10^9/t)

take the natural log of both sides and you get:

ln(0.55) = -4.5x10^9/t

Therefore t = -4.5x10^9/ln(0.55) = 7.527 billion years

This makes sense because we would expect 50% to be gone after 4.5 billion years, and 75% to be gone after about 9 billion years, so we know our value must life somewhere in between.

Hope this helps

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Dmagrino Author

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10 years ago

For some reason i keep getting the wrong answer. I'm not sure why

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padre

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10 years ago

OK here's another example

Example

You are analyzing Moon rocks that contain small amounts of uranium-238, which decays into lead with a half-life of about 4.5 billion years.

1)In a rock from the lunar highlands, you determine that 50% of the original uranium-238 remains, while the other 50% has decayed into lead. How old is the rock?

In a rock from the lunar maria, you find that 60% of the original uranium-238 remains, while the other 40% has decayed into lead. Is this rock older or younger than the highlands rock?

2.)The rock is younger, but by how much?

Answer

1) One half life has passed so the rocks have an age of 4.5 billion years

2) We have P(t) = 100% 2^(-t/T) , where T is the half life
In this case P(t)=60%. Take logarithms and rearrange to find
ln 0.6 = -t/T ln 2
t = - T ln 0.6 / ln 2 = 3.3 billion years

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