Question

In the laboratory small zircon crystals were separated from granite (K).
Isotopic analysis of these zircon crystals gives a 207Pb/235U ratio of 0.45. the half-life of 235U (7.04 × 108
years), estimate the age of the granite in Ma to two significant figures

Answer 1

I would start by turning this thing around so that (235U/207Pb) = 1/0.45 = 2.22

Then I would adjust the ratio to account for the fact that Pb has a lower atomic mass than U by a factor of 235/207 = 1.135 so 2.222/1.135 = 1.958.
For every x atoms U that decay to Pb, the Pb will be x and the U remaining will be 100-x; therefore,
[(100-x)/x] = 1.1958
Solve for x = (Pb) and (100-x) U.
Then (No/N) = kt
for No = 100
For N = what you found above for 100-x
k see below.
t = time.

k = 0.693/t<sub>1/2</sub.
k = 0.793/7.04E8

Answer 2

I'm going out on a limb here, and I know you might not reply, but, DrBob222, I need to ask you something concerning this.

Why did you flip the ratio? Wouldn't that effect the answer?

And is that a mistake in the middle where you said,

"Then I would adjust the ratio to account for the fact that Pb has a lower atomic mass than U by a factor of 235/207(!that is what I'm talking about!) = 1.135 so 2.222/1.135 = 1.958."

Shouldn't that be flipped? I ran it through a calculator and the flipped version gave '1.135' like you said the other version equalled here.