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 (11Ar). 
Then, the fractional abundance of the heavier isotope (11Ar) would be (1-x).

Using the formula for average atomic mass:
average atomic mass = (mass of isotope 1)(fractional abundance of isotope 1) + (mass of isotope 2)(fractional abundance of isotope 2)

Substituting the given values and solving for x:
107.8682 amu = (106.90509 amu)(x) + (108.9047 amu)(1-x)
x = 0.51835

Therefore, the fractional abundance of the lighter isotope is 0.51835.

Silver Has Two Naturally Occurring Isotopes with the Following Isotopic