Silver (ag) has two stable isotopes: 107ag, 106.90 amu, and 109ag, 108.90 amu. if the average atomic mass of silver is 107.87 amu,
what is the natural abundance of each isotope? (expressed as a percentage)
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Ответ:
Explanation:
The average atomic mass of silver can be expressed as:
107.87 = 106.90 * A1 + 108.90 * A2
Where A1 is the abundance of 107Ag and A2 of 109Ag.
Assuming those two isotopes are the only one stables, we can use the equation:
A1 + A2 = 1.0
So now we have a system of two equations with two unknowns, and what's left is algebra.
First we use the second equation to express A1 in terms of A2:
A1 = 1.0 - A2
We replace A1 in the first equation:
107.87 = 106.90 * A1 + 108.90 * A2
107.87 = 106.90 * (1.0-A2) + 108.90 * A2
107.87 = 106.90 - 106.90*A2 + 108.90*A2
107.87 = 106.90 + 2*A2
2*A2 = 0.97
A2 = 0.485
So the abundance of 109Ag is (0.485*100%) 48.5%.
We use the value of A2 to calculate A1 in the second equation:
A1 + A2 = 1.0
A1 + 0.485 = 1.0
A1 = 0.515
So the abundance of 107Ag is 51.5%.
Ответ:
I hope you won't be solid on this answer, But I researched it with my colleagues, and we all agreed it's the amount of atoms in the compound. (I hope this was you question.)