Moon rocks contain small amounts of uranium-238, which decays into lead with a half-life of 4.5 billion years. In one rock, you determine that 60% of the original uranium-238 remains, while the other 40% has decayed into lead. How old is the rock?

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Answer 1 · 2016-04-21T12:00:10

3.3 billion years,

In both the rocks, 60% remains.

If m% of mass remains now after T billion years,

#m=ce^(-kT)#, where c and k are constants for the radioactive material that is decaying.,

When T = 0, m = 100 and when m=50, T = 4.5,

So, #c = 100 and 50 = 100 e^(-4.5k)#.

So, #e^(-4.5k)=1/2 and k = ln 2/4.5=0.1540#.

Now,# m=100e^(-0.154 T)#
Inversely, #T=ln(100/m)/0.154#. .

For the rock that had lost 40%, 60% remains. Its age T is given by
#T = ln(100/60)/0.154=3.3# billion years, nearly.