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 this rock?

Answer 1

2.5 x `10^9` yrs old

Explanation:

Given K-40 remaining = 25% of original K-40 @ 100%
`t_(1/2) = 1.251x10^9 yrs` => `k = 0.693/t_(1/2)`
`k=0.693/(1.251x10^9) yrs^-1=5.54x10^-10yrs^-1`

From `C_("final") = C_("initial")e^-"k.t"`; t = time of decay

Solving for time of decay (t) `= ln(C_("final")/C_"initial")/-k`

`t = (ln(25/100)/-(5.54x10^-10))` years old = 2.5 x `10^9` yrs old