The ratio of carbon-14 to carbon-12 in the shaft of a wooden arrow, unearthed when a foundation was being dug for a new house, is 56.0% of the same ratio in a growing tree today. Assuming the ratio of carbon-14 to carbon-12 in the atmosphere has been constant, calculate the age of the arrow. The half-life of carbon-14 is 5730 years. The arrow is years old Numeric

The wooden arrow is    old

Explanation:

From the question we are told that

  The ratio of carbon -14 to carbon- 12  is  %

   The half - life of carbon 14 is

Generally half-life is mathematically evaluated as

Where   is the decay constant

    making  the subject of the formula

Now the age of the  wooden arrow can be mathematically obtained

 The initial amount of is  

The amount  remaining in the  wooden arrow is

           %

substituting values

"you start with 15.67 g mgco3-xh2o, when heated and all the water is removed, you are left with 7.58 g mgco3 only.

therefore, you had 15.67 - 7.58 = 8.09g h2o  

moles of each :

7.58g mgco3 = ? moles = 7.58g / 83.4g/mole = 0.09moles  

8 09g h2o = ? moles = 8.09g / 18g/mole = 0.44moles  

molar ratio between the two by dividing both numbers by the smallest number :

0.09 / 0.09 = 1  

0.44 / 0.09 = 4.8  

mgco3-5h2o"