Question

A sample of rock is found to have a parent-to-daughter isotope ratio of 1:3. Assume all the isotope in the original rock was parent isotope and that the half-life of the parent isotope is 5 million years. What is the age of the rock?

a) less than 5 million years old
b) 5 million years old
c) 10 million years old
d) 15 million years old
e) 20 million years old

Answer 1

for a first order reaction; we have the relation -KE At= Ao e In At = ln Au-kt Kt = lnto - ln At = ln Alar kh I In to At tiz 5 million : 0.693 K years :k= 0.693 ] 5 million years rate constant Ao = Initial amount = 100% At: Annusmy lyf = (100-75)&= 25% (75.). in daughter isotope formed to Smillion years In loot 0.693 ta 5million 10 million years x lu (4) 0.693 years Hence; age of the rock (t) is 10 million old. years