Question

An ancient rock is found to contain 40Ar gas, indicating that 77% of the 40K in the rock has decayed since the rock solidified. Any argon would have boiled out of liquid rock. How long ago did the rock solidify? The half-life of 40K is 1.25 billion years.

A) 2.6 billion years

B) 0.5 billion years

C) 1.8 billion years

D) 0.3 billion years

Answer: A

Answer 1

The amount left after t billion years is

(1/2)^(t/1.25)

So, you want

(1/2)^(t/1.25) = 0.77
t/1.25 log 0.5 = log 0.77

t = 1.25 log(0.77)/log(0.5) = 0.471

Looks like (B) to me.