Question

You pick up a rock and measure that it has 400 parent atoms and 1200 daughter atoms. If the half life of the parent is 5000 years, how old is the rock?

Answer 1

10,000 years.

Explanation:

∵ Number of parent atoms = 400,

Number of daughter atoms = 1200,

So, the proportional of parent atoms =
`(400)/(1200)` = 0.25 = 25 %

Since, 25% proportion of parent atoms shows there are two half lifes,

Given,

The number of years in one half life = 5000,

Hence, the age of the rock = 2 × 5000 = 10,000 years.

Answer 2

The rock is 6609.5 years old

Explanation:

Given :You pick up a rock and measure that it has 400 parent atoms and 1200 daughter atoms

To Find :If the half life of the parent is 5000 years, how old is the rock?

Solution:

Formula :
`\text{Amount remaining}=\frac{\text{original amount}}{2^n}`

Let A be the amount remaining

Let
`A_0` be the original amount

So.
`A=(A_0)/(2^n)`

`(A_0)/(A)=2^n`

We are given that it has 400 parent atoms

So, if there were 1000 atoms originally then 400 are remaining

`(1000)/(400)=2^n`

`(5)/(2)=2^n`

`\log((5)/(2))=n\log 2`

`(\log((5)/(2)))/(\log 2)=n`

`1.3219=n`

So, t =
`t_{(1)/(2)}* 1.3219`

t =
`5000* 1.3219`

t =
`6609.5`

Hence the rock is 6609.5 years old