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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
N  N0 e
 t
N 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)