Suppose you find a rock that contains 10 micrograms of radioactive potassium-40, which has a half-life of 1.25 billion years. by measuring the amount of its decay product (argon-40) present in the rock, you conclude that there must have been 80 micrograms of potassium-40 when the rock solidified. how old is the rock?

The rock is 3.75 billion years ago.

Explanation:

Given that:

Half life = 1.25 billion years

1 billion years = 10⁹ years

So,

Half life = 1.25 × 10⁹ years

Where, k is rate constant

So,  

The rate constant, k = 5.5452 × 10⁻¹⁰ years⁻¹

Initial amount [A₀] = 80 micrograms

Final amount = 10 micrograms

Using integrated rate law for first order kinetics as:

So,  

So,

The rock is 3.75 billion years ago.

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