Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Fundamentals Of Physics
Found in: Page 1306

Answers without the blur.

Just sign up for free and you're in.


Short Answer

The isotope K40 can decay to either C40a or A40r; assume both decays have a half-life of 1.26×109 y. The ratio of the Ca produced to Ar the produced is 8.54/1 = 8.54. A sample originally had only K40. It now has equal amounts of K40 and A40r; that is, the ratio of K to Ar is 1/1 = 1. How old is the sample? (Hint: Work this like other radioactive-dating problems, except that this decay has two products.)

The sample is 4.24×109y old.

See the step by step solution

Step by Step Solution

Step 1: Given data

Half-life of 40Ca and 40Ar, T1/2=1.26×109 y

Ratio of Ca to Ar is Nca/Nk=8.54/1.

Ratio of K to Ar is NAr/Nk=1.

Step 2: Understanding the concept of radioactive dating

The concept of radioactive dating is used to know the age of the fossil using the given decay rates. Here, the problem is of a parent nucleus that can decay into two products. Being the products of the decay, the number of atoms of calcium and argon were initially potassium atoms before the decay. Thus, the total number of initial potassium atoms can be given as the sum of all the three atoms present in the rock after the decay at the given time.


The disintegration constant, λ=ln2T1/2....(1)

where, T1/2 is the half-life of the substance.

The undecayed sample remaining after a given time, N=N0e-λt............(2)

Step 3: Calculation of the age of the sample

We note that every calcium-40 atom and krypton-40 atom found now in the sample was once one of the original numbers of potassium atoms.

Thus, the total number of initial potassium-40 atoms can be given as:


Thus, substituting equation (1) in (2) with the above data, we can get the age of the sample as follows:

lnNkNko=-ln 2T1/2tlnNkNk+NAr+Nca=-ln 21.26×109 yt ln11+1+8.54=-0.55501×10-9/yt ln110.54=0.55501×10-9/yt t=2.35520.55501×10-9/yt =4.24×109 y

Hence, the age of the sample is 4.24×109 y.

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.