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A fossil contains 2.60 mcg of pottasium-40. If the ratio of the radioactive element to decay...

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.
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Answer #1

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

\RightarrowAnswer:

The Age Of the fossil =    2.6 x 109 years:

\RightarrowExplanation:

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 : t1/2 = 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

\RightarrowWhere:

  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.

\RightarrowAssuming: 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 t1/2 = ( 2.0 ) x ( 1.3 x 109 years ) =  2.6 x 109 years:

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