Question

A fossil contains 2.60 mcg of pottasium-40. If the ratio of the radioactive element to decay is 1:4 (25-75%) how old is the fossil.

Answer 1

Following is the - complete Answer -&- Explanation: for the given Question: in....typed format...

$\Rightarrow$Answer:

The Age Of the fossil =    2.6 x 10⁹ years:

$\Rightarrow$Explanation:

Following is the complete Explanation: for the above Answer.

• Given:

1. Mass of potassium - 40: in the fossil = 2.60 microgram = 2.6 x 10 ^-6 g ( grams )
2. Ratio of original radioactive element : dacay = 1:4 i.e. 25% : 75%
3. We know: the Half life : t_1/2 = 1.3 x 10⁹ years: for radioactive isotope: K-40

• Step - 1:

​​​​​​​We know the following formula: i.e. of Half Life:

$\Rightarrow$ ( mass of radioactive element remaining after decay ) = 1/ 2ⁿ x ( Original mass of radioactive element ) --Equation - 1

$\Rightarrow$Where:

1. n = Number of half lives : passed.

• ​​​​​​​Step - 2:

​​​​​​​Since, we know: after 75% decay: the mass of radioactive element remaining = ( 100% - 75% ) = 25% after decay.

$\Rightarrow$Assuming: original mass of K-40 = 100%

Now, plugging in values: in ...Equation - 1: we would get:

$\Rightarrow$ ( 25.0 % ) = ( 1/2 )ⁿ x ( 100% )

$\Rightarrow$    ( 1/2 )ⁿ =   ( 25.0%) / (100.0%) = 1/4 =   ( 1/2 ) ²

Therefore: we get:

$\Rightarrow$  n = 2 ( i.e. two half lives )

• Step - 3:

Therefore:

$\Rightarrow$ Age of the fossil = n x t_1/2 = ( 2.0 ) x ( 1.3 x 10⁹ years ) =  2.6 x 10⁹ years: