Question

a rock is examined to determine its age, and the ratio of uranium-235 to lead-207 is found to be 125,000:875,000. the half-life of uranium-235 is 700 million years. how old is the rock being examined?

Answer 1

The old age of rock when examined is 21.4 million years if the ratio of uranium-235 to lead-207 is found to be 125,000:875,000. the half-life of uranium-235 is 700 million years.

Decaying Equation

P = [P + D] (1/2) ^(t/t(1/2))

where,

P represent the present parent amount

D is the present daughter amount

t(1/2) is the half life time period

t is the actual age

We know that,

t = (log[(P+D) /P] / log2) × t(1/2) ----------(1)

Given,

P = 97.6

D = 2.1

Ratio of P and D can be calculated as

P/D = 97.6/2.1

= 46.476

By substituting all the values in eq(1), we get

t = [(log 46.476 +1)/log2] × t(1/2)

Given,

The half life of U —Pb decay is 700 million years.

So,

t = [(log 46.476 +1)/log2] × 700

t = 21.4 million years.

Thus, we calculated that the the old age of rock when examined is 21.4 million years.

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The given question is misprint on portal.

Here is the correct form of question:

A rock is examined to determine its age, and the ratio of uranium-235 to lead-207 is found to be 125,000:875,000. the half-life of uranium-235 is 700 million years.

How old is the rock if it contains Uranium-235/ lead-207 ratio of 97.6 to 2.1?