Numberman Strikes Back

Richard Dawkins gives a nice account of radioisotope dating in "The Redwoods Tale." Until he comes to actual numbers. After explaining that potassium 40 decays to argon 40 with a half-life of 1.3 billion years, he explains how you can do dating by comparing the amounts of the respective isotopes left in the rock.

If there are equal amounts of potassium 40 and argon 40, you know that [half has decayed and the crystal formed 1.3 Gya]...
If there's twice as much argon 40 as potassium 40, it is 2.6 billion years . . .

Oops! If it were 2.6 gya, then only 1/4 of the potassium would have survived, and the ratio would be three to one, not two to one. He doesn't give the equation, but it can be written as:
N(t)=N0*2^(-t/h), where N(t) is the number of atoms at time t, N0 is the starting number and h is the half life. For his example N(t)/N0 = 1/3, so 2^(-t/h)=1/3 and (-t/h)*ln(2)= ln(1/3), or t= h*ln(3)/ln(2) = 2.06 billion years.

Similarly, he claims that if there is twice as much potassium as argon, the the crystal would be 650 million years old. Oops again. In that case N(t)/N =2/3 and t = h*ln(3/2)/ln(2) = .585 h = 760 million years.

Don't let Dawkins near the radioisotopes! Don't let him near any number larger than 2! You would think that he would let somebody who passed freshman physics read his manuscripts, but he never learns.