The technique known as potassiumargon dating is used to date

The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion year half-life and is naturally present at very low levels. 40K decays by two routes: 89% undergo beta-minus decay into 40Ca while 11% undergo electron capture to become 40Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of 40K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the 40Ar/40K ratio to be 1.0×102. What is the age of the rock?

Solution

From

N=N_oe^-t/T

Given N/N_o =1-0.01 =0.99

e^-t/T=0.99

-t/T=ln(0.99) =-0.01005

since T=t_1/2/Ln(2)

=>t =0.01005t_1/2/Ln(2)

t=0.01005*(1.28*10⁹)/Ln(2)

t=1.856*10⁷ years or 18.56 Myrs