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

2139 Million years

Step-by-step 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 =
`(26)/(3.25)  = (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) (R_(0) )/(R)`

where
`R_(0)` is the initial amount of material and R is the final amount

∵ Number of half lives =
`log_(2) (26 )/(3.25)`

= 3

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

=713000000 X 3

= 2139000000

=2139 Million Years