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fredd [130]
3 years ago
9

Use Table 1: Analysis of Decay in the laboratory guide to answer this question: Scientists find a piece of wood that is thought

to be from an ancient fire circle. They find that the wood contains an amount of carbon-14 (14C) that is approximately 1/16 of the current atmospheric 14C levels. Determine approximately how many years ago the tree was chopped down to be used for the firewood. If you started with 1 million carbon-14 atoms, how many atoms would remain in the wood? 14C has a t1/2 of 5,750 years.
Chemistry
1 answer:
Sladkaya [172]3 years ago
6 0
<span>We are given the initial amount of 1 million carbon-14 atoms and the final amount which is 1/16 of the current atmospheric 14C levels. Also, the half life of carbon is </span>5,750 years. WE can use the decay formula

Aₓ = A₀e^-(ln2/t1/2)t
1,000,000(1/16) = (1,000,000)e^-(ln2/5750)t
t = 23,000 years
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Po_{210} ^{84}  ⟶  Pb_{206} ^{82}+  + He_{4} ^{2}

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Half-life of  Po_{210} ^{84}  (T(1/2)) = 138.4 days

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Avogadro’s number: This is the number of constituent particles that are contained in a mol of any substance. These constituted particles can be atoms, molecules or ions). Its value is 6.023*10^23.  

The radioactive decay law is  

N=Noe^(-λt)

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No = number of atoms in t=0

N = number of atoms in t=t (now) in this case t=338.8 days  

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λ= \frac{ln2}{138.4 days}  =0,005008 days^(-1)

No (Atoms of  Po_{210} ^{84}  in t=0)

To get No we need to calculate the number of atoms of  Po_{210} ^{84}   in the initial sample. We have a sample of 0,561 g of PoCl4. If we get the number of moles of PoCl4 in the sample, this will be the number of moles of  Po_{210} ^{84}  in the initial sample.  

This is:

\frac{0,561 g of PoCl4}{350. 79 g of PoCl4 /mol} = 0,001599 mol of  PoCl4

This is the number of mol of  Po_{210} ^{84} in the initial sample.

To get the number of atoms in the initial sample we use the Avogadro’s number = 6.023*10^23  

0,001599 mol of  Po_{210} ^{84} * 6.023*10^23 atoms/ mol of  Po_{210} ^{84} = 9.632 *10^20 atoms of  Po_{210} ^{84}

Atoms after 338.8 days

We use the radioactive decay law to get this value  

N=Noe^(-λt)

N=9.632*10^20 e^(-0,005008 days^(-1) * 338.8 days) =1.765*10^20

This is the number of atoms of  Po_{210} ^{84} in the sample after 338.8 days has passed  

The number of atoms  Po_{210} ^{84} transformed is equal to the number of atoms of Pb_{206} ^{82}  produced.  

The number of atoms of Po_{210} ^{84} transformed is No - N  

9.632 *10^20 – 1.765 *10^20 = 7.866*10^20

So, 7.866*10^20 is the number of atoms of Pb_{206} ^{82} produced  

We can get the mass with the Avogadro’s number

(7.866*10^20 atoms of Pb_{206} ^{82} ) / ( 6.023*10^23 atoms of Pb_{206} ^{82} / mol of Pb_{206} ^{82} =  0.001306 moles of Pb_{206} ^{82}

This number of moles have a mass of:

(0,001306 moles of Pb_{206} ^{82} )* (205.97 g of Pb_{206} ^{82} /mol of Pb_{206} ^{82} ) = 0.269 g  

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