Question

Suppose you found a material in which 12.5% of the orginal radioactive atomes were present. if the half is 470 years, how old is the material

Answer 1

Answer:

1410years

Explanation:

$M_{R} =\frac{M_{O} }{2^{n} }$   ..........................equ 1

      $n=\frac{t}{t_{1/2} }$

where $M_{R}$ = mass remaining

          $M_{O}$ = Original mass.  

          t=time

           $t_{1/2}$= half life

  $M_{R} =12.5% of M_{O}$

 $M_{R} =0.125M_{O}$

Substitute $M_{R} =0.125M_{O}$ into equ 1

$0.125M_{O}=\frac{M_{O} }{2^{n} }$

$2^{n}=\frac{100}{12.5} \\2^{n}=8\\\\2^{n}=2^{3}$

n=3

  $n=\frac{t}{t_{1/2} }$

     $t=t_{1/2}*n$

     t=470*3

     t=1410years