Question

Silver has two naturally occurring isotopes with the following isotopic masses: 10747Ag 10947Ag 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 ________.

Answer 1

Answer: The fractional abundance of lighter isotope is 0.518

Explanation:

Average atomic weight is the sum of the masses of the individual isotopes each multiplied by its fractional abundance. The equation used is:$\text{Average atomic weight}=\sum_{i=1}^{n}\text{(Atomic mass of isotope)}_i\times \text{(Fractional abundance)}_i$           ......(1)

Let the fractional abundance of Ag-107 isotope be 'x'

• For Ag-107 isotope:

Atomic mass = 106.90509 amu

Fractional abundance = x

• For Ag-109 isotope:

Atomic mass = 108.9047 amu

Fractional abundance = (1 - x)

Average atomic mass of silver = 107.8682 amu

Plugging values in equation 1:

$107.8682=(106.90509 \times x) + (108.9047 \times (1-x))\\\\107.8682=106.90509x+108.9047-108.9047x\\\\1.99961x=1.0365\\\\x=0.518$

Fractional abundance of Ag-107 isotope (lighter) = x = 0.518

Hence, the fractional abundance of lighter isotope is 0.518