Question

A rock contains 25 % of the parent isotope. The half-life of this isotope is 5 million years. Calculate the age of the rock. For your answer, just type the age.

Answer 1

The age of the rock 10.00 million years old.

Step-by-step explanation:

Half-life = 5 million years

First we have to calculate the rate constant, we use the formula :

`k=(0.693)/(t_(1/2))`

`k=\frac{0.693}{5\text{million years}}`

`k=0.1386\text{million years}^(-1)`

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(N_o)/(N)`

where,

k = rate constant =
`1.21* 10^(-4)\text{ years}^(-1)`

t = time passed by the sample or age of the sample = ?

`N_o` = let initial amount of the reactant = x

N= amount left after decay process = 25% of x =0.25 x

`t=\frac{2.303}{0.1386\text{million years}^(-1)}\log(x)/(0.25)`

`t=10.00 \text{million years}`

The age of the rock 10.00 million years old.