Question

The half-life of uranium-235 is 713 million years. Suppose a rock originally had 26 grams of uranium-235. A geologist had the rock tested, and found that it now has only 3.25 grams of uranium-235.
Approximately how old is the rock?

Answer 1

Answer:

2139 Million years

Explanation:

Half life of a material is the time required for the material to decay into half of initial amount.

initially there is 26 grams of uranium-235, and the final amount is 3.25 gram

                 ratio between initial and final amount = $\frac{26}{3.25} = \frac{1}{8}$

now it is clear that the material have halved 3 times from initial condition

number of half lives passed = 3

number of half lives passed can also be found using the equation

                no of half lives = $log_{2} \frac{R_{0} }{R}$

where $R_{0}$ is the initial amount of material and R is the final amount

∵ Number of half lives = $log_{2} \frac{26 }{3.25}$

                                      = 3

So, age of rock = half-life X number of half-lives passed

                          =713000000 X 3

                          = 2139000000

                          =2139 Million Years