Silver has two naturally occurring isotopes with the following isotopic masses: Ar Ar 106.90509 108.9047
The average atomic mass of silver is 107.8682 amu. The fractional abundance of the lighter of the two isotopes is __________.

Question

Silver has two naturally occurring isotopes with the following isotopic masses:  Ar  Ar 106.90509 108.9047
The average atomic mass of silver is 107.8682 amu. The fractional abundance of the lighter of the two isotopes is __________.

Quizplus · Accepted Answer

Let x be the fractional abundance of the lighter isotope (with mass 106.90509 amu). 
Then, the fractional abundance of the heavier isotope (with mass 108.9047 amu) must be 1-x.

Using the formula for calculating average atomic mass:

average atomic mass = (mass of isotope 1) x (fractional abundance of isotope 1) + (mass of isotope 2) x (fractional abundance of isotope 2)

Substituting in the given values and solving for x:

107.8682 amu = (106.90509 amu) x (x) + (108.9047 amu) x (1-x)

107.8682 amu = 106.90509x + 108.9047 - 108.9047x

Simplifying:

x = 0.51835

Therefore, the fractional abundance of the lighter isotope is 0.51835 or 51.835%. 
The answer is choice C.

Silver Has Two Naturally Occurring Isotopes with the Following Isotopic