Question

Radioactive decay of 40K atoms in an igneous rock has resulted in a ratio of 25 percent 40K atoms to 75 percent 40AR and 40CA atoms how many years old is the this rock

Answer 1

The answer is 6×10⁹ years.

K-Ar dating is radioactive dating method used to measure a time elapsed since the rock is cool enough to trap Ar after a radioactive decay of 40K to 40Ar. It can be expressed as:

`t= \frac{ t_{ (1)/(2) } }{ln(2)} ln( ( K_(f) + ( Ar_(f) )/(0.109) )/( K_(f) ) )`
where:

`t` - elapsed time

`t_{ (1)/(2) }` - half-life of K40

`K_(f)` - amount of K40

`Ar_(f)` - amount of Ar40

We know that a half-life of K40 is 1.251×10⁹ years:

`t_{ (1)/(2) } =1.251* 10^(9)`

We do not know absolute value of amount of K40 and Ar40, but we know percentage and can express them as following:

`K_(f) =25%=0.25`

`Ar_(f) =75%=0.75`

So:

`t= (1.251* 10^(9) )/(ln(2)) ln( (0.25+ (0.75)/(0.109) )/(0.25) )`

⇒ t = 6×10⁹

Thus, the rock is old 6×10⁹ years.