Quiz 5
Ryan Richards
You have a rock that today contains 3 atoms of 40Ar for every atom of
40
K. When the rock solidified, it contained no 40Ar. The half-life of 40K
is 1.25 Gyr. The age of the rock is_______
The formula for the amount of 40Ar atoms is
!
B = B0 + A0 (1-( )! )
!
Where A0 is the initial amount of 40K atoms, B0 is the initial amount 40Ar
atoms, which in our case is zero, and τ is the number of half-lives. We
will take A0 to be 1 for simplicity.
Now a half-life is refers to the amount of time it takes for the number of
40
K atoms to reduce in half.
After one half-life i.e., τ = 1, the simple calculation gives B of equal to
½. We also have A equal to ½ also. Therefore the ratio is ½ : ½ or 1:1.
That is 1 atom of 40Ar for every one atom of 40K. What we want is a
3:1 ratio.
When 𝜏 = 2, we have B equal to ¾ and A is now equal to half of half
which is a 1/4. The ratio becomes 3/4:1/4 or 3:1.
So that means that it takes 2 half-lives for the ratio of 40Ar to 40K to be
3:1.
Therefore we conclude the rock is 2.5 Gyr.