Arock contains 0.275 mg of lead-206 for each milligram of uranium-238. the for the decay of uranium-238 to lead-206 is 4.5 x 10 9 yr. the rock was formed yr ago.

The rock is formed years ago.

Explanation:

Given that:

Half life = years

Where, k is rate constant

So,  

The rate constant, k = years⁻¹

Using integrated rate law for first order kinetics as:

Where,  

is the final concentration= 0.275 mg

is the initial concentration = 1 mg

Let = 1 mg

A rock contains 0.275 mg of lead-206 for each milligram of uranium-238. So,

= mg = 1.297 mg

Time = ?

So,  

years

The rock is formed years ago.

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