Question

The ages of rocks that contain fossils can be determined using the isotope 87Rb. This isotope of rubidium undergoes beta

decay with a half-life of 4.75 x 101ºy. Ancient samples contain a ratio of 87 Sr to 87Rb of 0.0105. Given that 87Sr is a stable
product of the beta decay of 87Rb, and assuming there was originally no 87 Sr present in the rocks, calculate the age of the
rock sample. Assume that the decay rate is constant over the relatively short lifetime of the rock compared to the half-life of
87Rb.

Answer 1

Age of rock = 722 million years old

Step-by-step explanation:

Using the formula; fraction remaining = 0.5ⁿ

where n = number of half lives elapsed.

However, from the given values, fraction remaining = 1.000 - 0.0105

fraction remaining = 0.9895

Substituting in the formula to determine the number of half-lives:

0.9895 = 0.5ⁿ

log 0.9895 = n log 0.5

-0.0045842 = -0.30103 n

number of half lives elapsed, n = 0.0152

Therefore age of rock = 0.0152 x 4.75 x 10¹⁰ years = 7.22 x10⁸ years

Age of rock = 722 million years old