Determination of the Age of the Earth (Second Method)

Radioactivity in the Earth’s Crust• One can find the age of a rock by

measuring the amount of radioactivity

• In particular one is interested in the daughter decay series

• K40 half life (T1/2 1277 million years)

• Isotopic Abundance 0.118 %

• Age of earth about 4 billion years

Second Method Uranium and Actinium decay series

• U238 T1/2 = 4468 million years

• U235 T1/2 = 703.8 million years

• Both of these isotopes are not made in stars. They are “Transuranic Elements”

• Probably made during big bang and in Supernovae explosions

• Assume original abundance of these two isotopes were the same

Radioactive Decay

• Radioactive Decay is a logarithmic decay

teNN 0N is the number of atoms after a time t

N0 is the original number of atoms at time 0

is the decay constant

t is the elapsed time

= lne2 /T1/2 = 1/(1.44 T1/2) (Can be either years or seconds)