Question

Suppose a scientist finds a rock with an interesting fossil. Curious to know the age of the fossil, she takes the rock to a lab. The lab determines the amount of rubidium (Rb) and strontium (Sr) in the rock. The scientist is familiar with radiometric dating and knows that she can now calculate the age of the rock, t, using an isochron. The Rb-Sr isochron equation is STSIO + 365It 87 SIt -=86510 86 Srt - 87 Rbt colt _ 1] Using the lab's values, she calculates the isotope ratios aset = 3.807 and Robin = 89.60. In a published table, she finds that - 8TS10 - was 86 STO the ratio of strontium-87 to strontium-86 at the formation of the rock was 0 = 0.7129. She also finds that the decay constant, 1, for rubidium-87 is 1.42 x 10-11. Use the equation and provided data to calculate t. Put your answer in scientific notation and round to the nearest tenth. х100 years What is the approximate age of the rock in billions of years? Round to the nearest tenth. billions of years

Answer 1

We have;

, where;

8751 STROL ST sro + 36 Srt 365ro 86 Set

ST srt 86 Srt 3.80
   
81 Sro -0.7129 86 Sro
   
Si Rot 86 Srt -= 89.6

X= 1.42 x 10-11

Therefore,

3.807 = 0.7129 + 89.6 [e1.42x10-117_11

=> 3.0941 + 89.6 = 89.6 x 1.42x10-117

=> 89.6 x 1.42x 10-117 _

=> 1.42x10-114 92.6941 89,6

Taking the Natural Log of both sides of the equation

=> In(e1.42x10-1) = in 92.6941 89,6

In(92.6941 => t = 142 x 10-11 89.6

=> t = 0.0239081016866 x 1011

Rounding to the nearest Tenths, the age of the rock is 2.4 x 10⁹ years, or 2390810168.6 x 10⁰ years.

In Bilions of years, the age of the rock is 2.4 billion years