Chapter 4: Structure of the Atom

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Q
Structure of Atom

Question:

The average atomic mass of a sample of an element X is 16.2 u. What are the percentages of isotopes _{8}^{16}	extrm{X}and _{8}^{18}	extrm{X} in the sample?

Answer:

The average atomic mass is the average mass of the atoms in the naturally occurring sample of the element. The average atomic mass of an element is the sum of the mass of its isotopes each multiplied by its natural abundance. 

It is given that the average atomic mass of X is 16.2 u. Let the natural abundance of _{8}^{18}	extrm{X} be x % and _{8}^{16}	extrm{X} be left ( 100-x 
ight ) %.

16.2=18	imes frac{x}{100}+16	imes frac{100-x}{100}

1620=18	imes x+16	imes (100-x)

1620=18x+1600-16x

1620-1600=18x-16x

x=10

Percentage abundance of _{8}^{16}	extrm{X} = 100-10=90%

Therefore, the percentage abundance of oldsymbol{{color{Blue} _{8}^{16}	extrm{X}}} and oldsymbol{{color{Blue} _{8}^{18}	extrm{X}}} is 90% and 10 % respectively.


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