Aradioactive isotope has a half-life of 10,000 years. how old is the rock if the ratio of radioactive parent isotope to stable daughter isotope is 1: 3

The rock is 20004.2 years old.

Explanation:

All the radioactive reactions follow first order kinetics.

The equation used to calculate rate constant from given half life for first order kinetics:

We are given:

Putting values in above equation, we get:

We are given:

Ratio of parent isotope : daughter isotope = 1 : 3

Let us assume that the amount of parent isotope is 100 g

So, amount of daughter isotope formed is 75 g

Hence, the amount of parent isotope left = 100 - 75 = 25 g

The equation used to calculate time period follows:

where,

= initial mass of isotope  = 100 g

N = mass of the parent isotope left after the time = 25 g

t = time = ? years

k = rate constant =

Putting values in above equation, we get:

Hence, the rock is 20004.2 years old.

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