Considering the definition of atomic mass, isotopes and atomic mass of an element, sb121 has a percent natural abundance of 0.5726 or 57.26% and sb123 has a percent natural abundance of 0.4284 or 42.84%.
<h3>Definition of atomic mass</h3>
The atomic mass is obtained by adding the number of protons and neutrons in a given nucleus of a chemical element.
<h3>Definition of isotope</h3>
Isotopes are the chemical elements in which atomic numbers are the same, but the number of neutrons is different.
<h3>Definition of atomic mass</h3>
The atomic mass of an element is the weighted average mass of its natural isotopes.
This is, the atomic masses of elements are usually calculated as the weighted average of the masses of the different isotopes of each element, considering the relative abundance of each of them.
<h3>Percent natural abundance of each isotope</h3>
In this case, antimony has two naturally occuring isotopes, sb121 and sb123. You know:
- sb121 has an atomic mass of 120.9038 u.
- sb121 has a percent natural abundance of x.
- sb123 has an atomic mass of 122.9042 u.
- sb123 has a percent natural abundance of 1 -x (or, what is the same, the abundance is 100% - x%, since both isotopes form 100% of the element.)
- Antimony has an average atomic mass of 121.7601 u
The average mass of antimony is expressed as:
121.7601 u= 120.9038 u x + 122.9042 u× (1 -x)
Solving:
121.7601 u= 120.9038 u x + 122.9042 u - 122.9042 u x
121.7601 u - 122.9042 u= 120.9038 u x - 122.9042 u x
(-1.1441 u)= (-2.0014) x
(-1.1441 u)÷ (-2.0014)= x
<u><em>0.5726= x or 57.26%</em></u>
So, 1 -x= 1- 0.5716 → <u><em>1-x= 0.4284 or 42.84%</em></u>
<u><em /></u>
Finally, sb121 has a percent natural abundance of 0.5726 or 57.26% and sb123 has a percent natural abundance of 0.4284 or 42.84%.
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